1 Load packages
2 Functions
3 Load data
4 Species Richness
- 4.1 Prepare data
- 4.2 Bayesian Analysis
5 Survey Effort
6 Community composition
7 Detection probability
8 Session Info
9 Cite Packages

1 Load packages

Load packages needed for data manipulation and analyses.

library(tidyverse)  #for data wrangling etc
library(cmdstanr)   #for cmdstan
library(brms)       #for fitting models in STAN
library(standist)   #for exploring distributions - *******must come after tidyverse********
library(coda)       #for diagnostics
library(bayesplot)  #for diagnostics
library(DHARMa)     #for residual diagnostics
library(rstan)      #for interfacing with STAN
library(emmeans)    #for marginal means etc
library(broom)      #for tidying outputs
library(tidybayes)  #for more tidying outputs
library(HDInterval) #for HPD intervals
library(ggeffects)  #for partial plots
library(broom.mixed)#for summarising models
library(posterior)  #for posterior draws
library(ggeffects)  #for partial effects plots
library(patchwork)  #for multi-panel figures
library(bayestestR) #for ROPE
library(see)        #for some plots
library(reshape2)
library(vegan)
library(car)
library(ggvegan)
library(ggrepel)
library(GGally)
library(corrplot)
library(EcolUtils)
library(scales)
library(colorspace)
library(MuMIn)
library(knitr)
library(report)
library(ggridges)
library(gghalves)
library(loo)
library(performance)

2 Functions

Custom ggplot theme for visualisation.

my.theme <- function(){
  theme_classic() +
    theme(text = element_text(family = "Avenir Next"),
          axis.title.y = element_text(margin = margin(t = 0,r = 20,b = 0,l = 0)),
          axis.title.x = element_text(margin = margin(t = 20,r = 0,b = 0,l = 0)), 
          plot.margin = unit(c(5, 10, 5, 10), units = "mm"),
          strip.background = element_rect(fill = "#CCCCFF"),
          strip.text.x = element_text(size = 20),
          axis.title = element_text(size = 20),
          axis.text = element_text(size = 18),
          legend.text = element_text(size = 15),
          legend.title = element_text(size = 15))
}

3 Load data

reptile_data <- read.csv("reptile_data.csv")

4 Species Richness

4.1 Prepare data

Created an object with coordinates for each plot to assess the effect of latitude.

site <- c(rep("Duval",4), rep("Mourachan",4), rep("Tarcutta",4), rep("Wambiana",4), rep("Undara",4), rep("Rinyirru",4))
site.plot <- c("Duval.DryA","Duval.DryB","Duval.WetA", "Duval.WetB", "Mourachan.DryA", "Mourachan.DryB", "Mourachan.WetA", "Mourachan.WetB", "Tarcutta.DryA", "Tarcutta.DryB", "Tarcutta.WetA", "Tarcutta.WetB", "Wambiana.DryA", "Wambiana.DryB", "Wambiana.WetA", "Wambiana.WetB",  "Undara.DryA", "Undara.DryB", "Undara.WetA", "Undara.WetB", "Rinyirru.DryA", "Rinyirru.DryB", "Rinyirru.WetA", "Rinyirru.WetB")
lat <- c(-30.41734901, -30.40221297, -30.41803398, -30.40110799, -27.77898598, -27.77996097, -27.78425401, -27.77876303, -35.36852497, -35.37876002, -35.36012203, -35.36613797, -20.53070999, -20.526226, -20.53458997, -20.53051997, -18.18705803, -18.24565097, -18.18492902, -18.26552999, -15.05447703, -15.04400703, -15.04891698, -15.04438899)
long <- c(151.622667, 151.624706, 151.61276, 151.629483, 149.032006, 148.981, 149.021332, 148.970948, 147.696893, 147.703341, 147.697579, 147.707788, 146.113426, 146.110754, 146.103876, 146.101471, 144.539753, 144.553799, 144.5324, 144.556613, 144.256419, 144.242852, 144.261894, 144.26052)
wet.dry <- rep(c("dry", "dry", "wet", "wet"),6)

coord <- data.frame(site, site.plot, lat, long, wet.dry)

Summarised the total number of species per method for each plot across all sites.

reptile_summary <- reptile_data %>% 
  unite(site.plot, c(site, plot), sep = ".", remove = FALSE) %>% 
  select(-plot) %>% 
  group_by(site, site.plot, assessment.method) %>% 
  summarise(richness = length(unique(scientific.name))) %>% 
  ungroup() %>% 
  add_column(wet.dry = ifelse(.$site.plot %in% c("Duval.WetA", "Duval.WetB",
                                                 "Tarcutta.WetA", "Tarcutta.WetB",
                                                 "Mourachan.WetA", "Mourachan.WetB",
                                                 "Wambiana.WetA", "Wambiana.WetB",
                                                 "Undara.WetA", "Undara.WetB",
                                                 "Rinyirru.WetA", "Rinyirru.WetB"), "wet", "dry"))

The data frame was missing zero values for methods that didn’t capture any species at a given plot. The following adds zeros for those instances.

# Created object with all combinations of plots and methods to include zero values
plots <- unique(reptile_summary$site.plot)
methods <- unique(reptile_summary$assessment.method)
zeros <- crossing(plots, methods)

# Added reference column for future join 
zeros$plots.methods <- paste(zeros$plots, zeros$methods)

# Selected only columns relevant to join
reptile_summary2 <- reptile_summary %>% 
  select("site.plot", "assessment.method", "richness")

# Added reference column for future join 
reptile_summary2$plots.methods <- paste(reptile_summary2$site.plot, reptile_summary2$assessment.method)

# Joined objects to include zero values for methods across plots
reptile_summary_all <- merge(reptile_summary2, zeros, by = "plots.methods",
                             all.x = T, all.y = T) %>% 
  select("plots", "methods", "richness") %>% 
  replace(is.na(.), 0) %>% 
  rename(site.plot = plots, assessment.method = methods) %>% 
  left_join(coord, by = "site.plot") %>% 
  mutate(site = factor(site, levels = c("Tarcutta", "Duval", "Mourachan", "Wambiana",
                                        "Undara", "Rinyirru")),
         site.plot = factor(site.plot, levels = c("Tarcutta.DryA", "Tarcutta.DryB", "Tarcutta.WetA", "Tarcutta.WetB", "Duval.DryA", "Duval.DryB", "Duval.WetA", "Duval.WetB", "Mourachan.DryA", "Mourachan.DryB", "Mourachan.WetA", "Mourachan.WetB","Wambiana.DryA", "Wambiana.DryB", "Wambiana.WetA", "Wambiana.WetB", "Undara.DryA", "Undara.DryB", "Undara.WetA", "Undara.WetB", "Rinyirru.DryA", "Rinyirru.DryB", "Rinyirru.WetA", "Rinyirru.WetB")),
         assessment.method = factor(assessment.method, levels = c("pitfall", "funnel","incidentals","spotlighting","cover board","camera")),
         wet.dry = factor(wet.dry),
         richness = as.numeric(richness))

4.2 Bayesian Analysis

4.2.1 Priors

Defining priors for Bayesian models.

Priors for the intercept.

reptile_summary_all %>% summarise(median(log(richness)))

##   median(log(richness))
## 1              1.098612

#1.1
reptile_summary_all %>% summarise(mad(log(richness)))

##   mad(log(richness))
## 1           1.454177

#1.5

Priors for the slope.

log(sd(reptile_summary_all$richness))/apply(model.matrix(~assessment.method*lat, data = reptile_summary_all), 2, sd)

##                       (Intercept)           assessment.methodfunnel 
##                               Inf                         3.6955179 
##      assessment.methodincidentals     assessment.methodspotlighting 
##                         3.6955179                         3.6955179 
##      assessment.methodcover board           assessment.methodcamera 
##                         3.6955179                         3.6955179 
##                               lat       assessment.methodfunnel:lat 
##                         0.1921267                         0.1433234 
##  assessment.methodincidentals:lat assessment.methodspotlighting:lat 
##                         0.1433234                         0.1433234 
##  assessment.methodcover board:lat       assessment.methodcamera:lat 
##                         0.1433234                         0.1433234

#3.7

4.2.2 Fit model

4.2.2.1 Model 1

priors1 <- prior(normal(1.1,1.5), class  = "Intercept") +
  prior(normal(0,3.7), class = "b") +
  prior(student_t(3,0,3.7), class = "sd")

methods.form1 <- bf(richness ~ assessment.method*scale(lat, scale = FALSE) + (1|site/site.plot),
                 family = poisson(link = "log"))

methods.brm1 <- brm(methods.form1,
                  data = reptile_summary_all,
                  prior = priors1,
                  sample_prior = "only",
                  refresh = 0,
                  chains = 3, cores = 3,
                  iter = 5000,
                  thin = 5,
                  seed = 8,
                  warmup = 1000,
                  backend = 'cmdstanr',
                  save_pars = save_pars(all = TRUE))

## Running MCMC with 3 parallel chains...
## 
## Chain 1 finished in 0.2 seconds.
## Chain 2 finished in 0.2 seconds.
## Chain 3 finished in 0.2 seconds.
## 
## All 3 chains finished successfully.
## Mean chain execution time: 0.2 seconds.
## Total execution time: 0.3 seconds.

4.2.2.1.1 Predictions

methods.brm1 %>% ggpredict(~assessment.method|lat) %>% plot(add.data = TRUE)

methods.brm1 %>% ggpredict(~lat|assessment.method) %>% plot(add.data = TRUE)

4.2.2.1.2 Prior vs Posterior

methods.brm1b <- methods.brm1 %>%
  update(sample_prior = "yes",
         refresh = 0,
         seed = 8,
         cores = 3,
         backend = "cmdstanr",
         save_pars = save_pars(all = TRUE))

## Running MCMC with 3 parallel chains...
## 
## Chain 2 finished in 2.2 seconds.
## Chain 1 finished in 2.5 seconds.
## Chain 3 finished in 2.4 seconds.
## 
## All 3 chains finished successfully.
## Mean chain execution time: 2.4 seconds.
## Total execution time: 2.6 seconds.

4.2.2.1.3 Predictions

methods.brm1b %>% ggpredict(~assessment.method|lat) %>% plot(add.data = TRUE)

methods.brm1b %>% ggpredict(~lat|assessment.method) %>% plot(add.data = TRUE)

4.2.2.2 Model 2

priors2 <- prior(normal(1.1,1.5), class  = "Intercept") +
  prior(normal(0,3.7), class = "b") +
  prior(student_t(3,0,3.7), class = "sd")

methods.form2 <- bf(richness ~ assessment.method*scale(lat, scale = FALSE) + (1|site/site.plot),
                 family="negbinomial")

methods.brm2 <- brm(methods.form2,
                  data = reptile_summary_all,
                  prior = priors2,
                  sample_prior = "only",
                  refresh = 0,
                  chains = 3, cores = 3,
                  iter = 5000,
                  thin = 5,
                  seed = 8,
                  warmup = 1000,
                  backend = 'cmdstanr',
                  save_pars = save_pars(all = TRUE))

## Running MCMC with 3 parallel chains...
## 
## Chain 2 finished in 1.9 seconds.
## Chain 3 finished in 3.5 seconds.
## Chain 1 finished in 3.9 seconds.
## 
## All 3 chains finished successfully.
## Mean chain execution time: 3.1 seconds.
## Total execution time: 4.0 seconds.

4.2.2.2.1 Predictions

methods.brm2 %>% ggpredict(~assessment.method|lat) %>% plot(add.data = TRUE)

methods.brm2 %>% ggpredict(~lat|assessment.method) %>% plot(add.data = TRUE)

4.2.2.2.2 Prior vs Posterior

methods.brm2b <- methods.brm2 %>%
  update(sample_prior = "yes",
         refresh = 0,
         seed = 8,
         cores = 3,
         backend = "cmdstanr",
         save_pars = save_pars(all = TRUE))

## Running MCMC with 3 parallel chains...
## 
## Chain 1 finished in 3.1 seconds.
## Chain 3 finished in 3.0 seconds.
## Chain 2 finished in 3.1 seconds.
## 
## All 3 chains finished successfully.
## Mean chain execution time: 3.0 seconds.
## Total execution time: 3.2 seconds.

4.2.2.2.3 Predictions

methods.brm2b %>% ggpredict(~assessment.method|lat) %>% plot(add.data = TRUE)

methods.brm2b %>% ggpredict(~lat|assessment.method) %>% plot(add.data = TRUE)

4.2.2.3 Model 3

priors3 <- prior(normal(1.1,1.5), class  = "Intercept") +
  prior(normal(0,3.7), class = "b") +
  prior(student_t(3,0,3.7), class = "sd")

methods.form3 <- bf(richness ~ assessment.method*scale(lat, scale = FALSE) + (1|site/site.plot),
                 family="negbinomial2")

methods.brm3 <- brm(methods.form3,
                  data = reptile_summary_all,
                  prior = priors3,
                  sample_prior = "only",
                  refresh = 0,
                  chains = 3, cores = 3,
                  iter = 5000,
                  thin = 5,
                  seed = 1,
                  warmup = 1000,
                  control = list(adapt_delta=0.99),
                  backend = 'cmdstanr',
                  save_pars = save_pars(all = TRUE))

## Running MCMC with 3 parallel chains...
## 
## Chain 2 finished in 0.5 seconds.
## Chain 1 finished in 0.6 seconds.
## Chain 3 finished in 0.5 seconds.
## 
## All 3 chains finished successfully.
## Mean chain execution time: 0.5 seconds.
## Total execution time: 0.7 seconds.

4.2.2.3.1 Predictions

methods.brm3 %>% ggpredict(~assessment.method|lat) %>% plot(add.data = TRUE)

methods.brm3 %>% ggpredict(~lat|assessment.method) %>% plot(add.data = TRUE)

4.2.2.3.2 Prior vs Posterior

methods.brm3b <- methods.brm3 %>%
  update(sample_prior = "yes",
         refresh = 0,
         seed = 2,
         cores = 3,
         control = list(adapt_delta=0.99),
         backend = "cmdstanr",
         save_pars = save_pars(all = TRUE))

## Running MCMC with 3 parallel chains...
## 
## Chain 2 finished in 9.6 seconds.
## Chain 1 finished in 10.3 seconds.
## Chain 3 finished in 10.4 seconds.
## 
## All 3 chains finished successfully.
## Mean chain execution time: 10.1 seconds.
## Total execution time: 10.5 seconds.

4.2.2.3.3 Predictions

methods.brm3b %>% ggpredict(~assessment.method|lat) %>% plot(add.data = TRUE)

methods.brm3b %>% ggpredict(~lat|assessment.method) %>% plot(add.data = TRUE)

4.2.2.4 Compare Models

(l.1b <- methods.brm1b %>% loo())

## 
## Computed from 2400 by 144 log-likelihood matrix
## 
##          Estimate   SE
## elpd_loo   -265.4 11.2
## p_loo        16.6  2.2
## looic       530.9 22.4
## ------
## Monte Carlo SE of elpd_loo is 0.1.
## 
## Pareto k diagnostic values:
##                          Count Pct.    Min. n_eff
## (-Inf, 0.5]   (good)     140   97.2%   668       
##  (0.5, 0.7]   (ok)         4    2.8%   290       
##    (0.7, 1]   (bad)        0    0.0%   <NA>      
##    (1, Inf)   (very bad)   0    0.0%   <NA>      
## 
## All Pareto k estimates are ok (k < 0.7).
## See help('pareto-k-diagnostic') for details.

(l.2b <- methods.brm2b %>% loo())

## 
## Computed from 2400 by 144 log-likelihood matrix
## 
##          Estimate   SE
## elpd_loo   -266.6 11.2
## p_loo        15.8  2.1
## looic       533.2 22.3
## ------
## Monte Carlo SE of elpd_loo is 0.1.
## 
## Pareto k diagnostic values:
##                          Count Pct.    Min. n_eff
## (-Inf, 0.5]   (good)     140   97.2%   688       
##  (0.5, 0.7]   (ok)         4    2.8%   193       
##    (0.7, 1]   (bad)        0    0.0%   <NA>      
##    (1, Inf)   (very bad)   0    0.0%   <NA>      
## 
## All Pareto k estimates are ok (k < 0.7).
## See help('pareto-k-diagnostic') for details.

(l.3b <- methods.brm3b %>% loo())

## 
## Computed from 2400 by 144 log-likelihood matrix
## 
##          Estimate   SE
## elpd_loo   -266.4 11.1
## p_loo        15.8  2.1
## looic       532.9 22.1
## ------
## Monte Carlo SE of elpd_loo is 0.1.
## 
## Pareto k diagnostic values:
##                          Count Pct.    Min. n_eff
## (-Inf, 0.5]   (good)     143   99.3%   325       
##  (0.5, 0.7]   (ok)         1    0.7%   518       
##    (0.7, 1]   (bad)        0    0.0%   <NA>      
##    (1, Inf)   (very bad)   0    0.0%   <NA>      
## 
## All Pareto k estimates are ok (k < 0.7).
## See help('pareto-k-diagnostic') for details.

loo_compare(loo(methods.brm1b), loo(methods.brm2b), loo(methods.brm3b))

##               elpd_diff se_diff
## methods.brm1b  0.0       0.0   
## methods.brm3b -1.0       0.5   
## methods.brm2b -1.2       0.4

Model methods.brm1b was selected as best model based on loo estimates.

4.2.3 Diagnostics

methods.brm1b %>% hypothesis("scalelatscaleEQFALSE = 0") %>% plot

4.2.3.1 Trace plots

methods.brm1b$fit %>% stan_trace()

#### Autocorrelation plots

methods.brm1b$fit %>% stan_ac()

#### Rhat statistic

methods.brm1b$fit %>% stan_rhat()

#### Effective sampling size

methods.brm1b$fit %>% stan_ess()

#### Posterior predictive check plot

methods.brm1b %>% pp_check(type = "dens_overlay", ndraws = 200)

#### DHARMa residuals

set.seed(6)
preds <- posterior_predict(methods.brm1b,  ndraws=250,  summary=FALSE)
method.resids <- createDHARMa(simulatedResponse = t(preds),
                            observedResponse = reptile_summary_all$richness,
                            fittedPredictedResponse = apply(preds, 2, median),
                            integerResponse = TRUE)
method.resids %>% plot()

#### Dispersion test

method.resids %>% testDispersion()

## 
##  DHARMa nonparametric dispersion test via sd of residuals fitted vs.
##  simulated
## 
## data:  simulationOutput
## dispersion = 0.51865, p-value < 2.2e-16
## alternative hypothesis: two.sided

4.2.3.2 Zero-inflation test

method.resids %>% testZeroInflation()

## 
##  DHARMa zero-inflation test via comparison to expected zeros with
##  simulation under H0 = fitted model
## 
## data:  simulationOutput
## ratioObsSim = 1.1663, p-value = 0.368
## alternative hypothesis: two.sided

4.2.4 Investigation

4.2.4.1 Methods pairwise comparison for each site

newdata_lat <- with(reptile_summary_all,list(lat = c(-35.37876,-30.40221,-27.77876,
                                                     -20.53459,-18.26553,-15.04439)))

(diff.methods <- methods.brm1b %>%
  emmeans(~assessment.method|lat, at = newdata_lat) %>%
  regrid() %>% #to get on absolute scale: richness
  pairs() %>% 
  gather_emmeans_draws() %>% 
  mutate(Percent = 100 * (exp(.value)-1), f.change = exp(.value)) %>% 
  summarise("Average difference (%)" = median(Percent),
            "Average fractional change" = median(f.change),
            "Lower HDI" = HDInterval::hdi(f.change)[1],
            "Upper HDI" = HDInterval::hdi(f.change)[2],
            "Probability of difference" = sum(.value > 0)/n()) %>% #to see if there is any change
  arrange(lat) %>%
  rename("Site" = lat) %>% 
  mutate(Site = as.factor(Site)) %>%  
  mutate(Site = fct_recode(Site, "Tarcutta" = '-35.37876', "Duval" = '-30.40221',
                           "Mourachan" = '-27.77876', "Wambiana" = '-20.53459',
                           "Undara" = '-18.26553', "Rinyirru" = '-15.04439')))

## # A tibble: 90 × 7
## # Groups:   contrast [15]
##    contrast                   Site     Average…¹ Avera…² Lower…³ Upper…⁴ Proba…⁵
##    <fct>                      <fct>        <dbl>   <dbl>   <dbl>   <dbl>   <dbl>
##  1 pitfall - funnel           Tarcutta      14.4    1.14  0.0586    4.59   0.572
##  2 pitfall - incidentals      Tarcutta     940.    10.4   1.54     62.8    1    
##  3 pitfall - spotlighting     Tarcutta    1085.    11.9   1.53     66.6    1    
##  4 pitfall - cover board      Tarcutta    1423.    15.2   1.77     97.2    1    
##  5 pitfall - camera           Tarcutta    1451.    15.5   1.82    107.     1    
##  6 funnel - incidentals       Tarcutta     802.     9.02  1.31     47.5    1.00 
##  7 funnel - spotlighting      Tarcutta     930.    10.3   1.39     54.4    1    
##  8 funnel - cover board       Tarcutta    1241.    13.4   1.49     78.1    1    
##  9 funnel - camera            Tarcutta    1266.    13.7   1.56     81.3    1    
## 10 incidentals - spotlighting Tarcutta      13.0    1.13  0.467     2.30   0.642
## # … with 80 more rows, and abbreviated variable names
## #   ¹`Average difference (%)`, ²`Average fractional change`, ³`Lower HDI`,
## #   ⁴`Upper HDI`, ⁵`Probability of difference`

4.2.4.2 Methods pairwise comparison for the average latitude

(diff.meth.avg <- methods.brm1b %>%
  emmeans(~assessment.method|lat) %>% 
  pairs() %>% 
  gather_emmeans_draws() %>% 
  mutate(Percent = 100 * (exp(.value)-1), f.change = exp(.value)) %>% 
  summarise("Average difference (%)" = median(Percent),
            "Average fractional change" = median(f.change),
            "Lower HDI" = HDInterval::hdi(f.change)[1],
            "Upper HDI" = HDInterval::hdi(f.change)[2],
            "Probability of difference" = sum(.value > 0)/n()) %>% 
  select(-lat))

## # A tibble: 15 × 6
## # Groups:   contrast [15]
##    contrast                   Average differen…¹ Avera…² Lower…³ Upper…⁴ Proba…⁵
##    <fct>                                   <dbl>   <dbl>   <dbl>   <dbl>   <dbl>
##  1 pitfall - funnel                         2.41    1.02   0.803    1.27   0.588
##  2 pitfall - incidentals                  149.      2.49   1.79     3.40   1    
##  3 pitfall - spotlighting                 204.      3.04   2.13     4.18   1    
##  4 pitfall - cover board                  380.      4.80   3.09     7.12   1    
##  5 pitfall - camera                      1089.     11.9    6.39    20.1    1    
##  6 funnel - incidentals                   145.      2.45   1.76     3.35   1    
##  7 funnel - spotlighting                  196.      2.96   2.07     4.09   1    
##  8 funnel - cover board                   369.      4.69   2.94     6.98   1    
##  9 funnel - camera                       1056.     11.6    6.36    20.0    1    
## 10 incidentals - spotlighting              20.9     1.21   0.787    1.81   0.812
## 11 incidentals - cover board               93.0     1.93   1.11     2.97   0.997
## 12 incidentals - camera                   374.      4.74   2.52     8.61   1    
## 13 spotlighting - cover board              58.3     1.58   0.944    2.56   0.966
## 14 spotlighting - camera                  294.      3.94   1.89     6.73   1    
## 15 cover board - camera                   148.      2.48   1.14     4.38   0.998
## # … with abbreviated variable names ¹`Average difference (%)`,
## #   ²`Average fractional change`, ³`Lower HDI`, ⁴`Upper HDI`,
## #   ⁵`Probability of difference`

4.2.5 Summary Plot

methods.em <- methods.brm1b %>%
  emmeans(~assessment.method|lat) %>% 
  pairs() %>% 
  gather_emmeans_draws() %>% 
  mutate(rate = exp(.value))

(methods.mag <- methods.em %>% 
  ggplot() + 
  geom_density_ridges_gradient(aes(x=rate, y=fct_reorder(contrast,rate)),
                               alpha = 0.4, col = "white",
                               quantile_lines = TRUE, quantiles = c(0.025, 0.975),
                               show.legend = FALSE, fill = "#05596E") +
  geom_vline(xintercept = 1, linetype = "dashed") +
  scale_x_continuous("Fractional change", trans = scales::log2_trans(),
                     breaks = c(1, 2, 5, 10, 50)) +
  scale_y_discrete(name = "") +
    my.theme())

## Warning: Using the `size` aesthetic with geom_segment was deprecated in ggplot2 3.4.0.
## ℹ Please use the `linewidth` aesthetic instead.

lat.list <- with(reptile_summary_all, list(lat = seq(min(lat), max(lat), length = 100)))

newdata <- emmeans(methods.brm1b, ~lat|assessment.method, at=lat.list, type = "response") %>%
  gather_emmeans_draws() %>%
  mutate(richness = exp(.value)) %>%
  group_by(lat, .draw) %>%
  mutate(sum_rate = sum(richness)) %>%
  ungroup() %>%
  mutate(proportion = richness/sum_rate) %>%
  filter(.draw %in% sample(1:2400, 200))

newdata3 <- emmeans(methods.brm1b, ~lat|assessment.method, at=lat.list, type = "response") %>% 
  as.data.frame %>% 
  group_by(lat) %>% 
  mutate(sum_rate.avg = sum(rate),
         proportion.avg = rate/sum_rate.avg) %>% 
  ungroup()

reptile_summary_all_prop <- reptile_summary_all %>% 
  group_by(lat) %>% 
  mutate(sum_rich = sum(richness),
         proportion = richness/sum_rich)


(methods.spag <- newdata %>% 
  ggplot() +
  geom_jitter(data = reptile_summary_all_prop, aes(x = lat, y = proportion, col = assessment.method),
              height = 0, width = 0.2, alpha = 0.4) +
  geom_line(aes(lat, proportion, col = assessment.method, group = interaction(assessment.method,.draw)), alpha=0.07) +
  geom_line(data = newdata3, aes(lat, proportion.avg, group = assessment.method), linewidth = 1.7, col = "black") +
  geom_line(data = newdata3, aes(lat, proportion.avg, col = assessment.method), linewidth = 1) +
  my.theme() +
  scale_y_continuous(name = "Proportion of total species richness",
                     labels = scales::percent,
                     breaks = seq(0, 0.5, by = 0.1),
                     limits = c(-0.025,0.5)) +
  scale_x_continuous(name = "", breaks=c(-35,-30,-25,-20,-15),
                     labels=c("35ºS", "30ºS", "25ºS", "20ºS", "15ºS")) +
  scale_fill_manual(values = c("#FF8300", "#D14103","#0CC170","black","#4E84C4","#8348D8"),
                      name = "Sampling Methods", labels = c("Pitfall Trap","Funnel Trap","Incidental","Spotlighting","Arboreal Cover Board","Camera Trap")) +
  scale_colour_manual(values = c("#FF8300", "#D14103","#0CC170","black","#4E84C4","#8348D8"),
                      name = "", labels = c("Pitfall Trap","Funnel Trap","Incidental","Spotlighting","Arboreal Cover Board","Camera Trap")) +
  theme(legend.text = element_text(margin = margin(t = 5)),
        legend.position = c(y=0.5, x=-0.07),
        legend.background = element_rect(fill = "transparent")) +
  guides(colour = guide_legend(nrow = 1)) +
  annotate("text", x = c(-35.37876,-30.40221,-27.77876,-20.53459,-18.26553,-15.04439),
           y = c(rep(-0.025, 6)),
           label = c("Tarcutta","Duval","Mourachan","Wambiana","Undara","Rinyirru")))

## Warning: Removed 3 rows containing missing values (`geom_point()`).

## Warning: Removed 4 rows containing missing values (`geom_line()`).

4.2.6 Report

report(methods.brm1b)

## Warning: Response residuals not available to calculate mean square error. (R)MSE
##   is probably not reliable.

## Warning in text == "" | text2 == "": longer object length is not a multiple of
## shorter object length

## Warning in text == "" | text2 == "": longer object length is not a multiple of
## shorter object length

## Running MCMC with 3 sequential chains...
## 
## Chain 1 finished in 1.9 seconds.
## Chain 2 finished in 1.9 seconds.
## Chain 3 finished in 1.9 seconds.
## 
## All 3 chains finished successfully.
## Mean chain execution time: 1.9 seconds.
## Total execution time: 5.8 seconds.

## Warning: Response residuals not available to calculate mean square error. (R)MSE
##   is probably not reliable.

## We fitted a Bayesian poisson mixed model (estimated using MCMC sampling with 3
## chains of 5000 iterations and a warmup of 1000) to predict richness with
## assessment.method (formula: richness ~ assessment.method * scale(lat, scale =
## FALSE)). The model included site.plot as random effects (formula: list(~1 |
## site.plot:site, ~1 | site)). Priors over parameters were set as normal (mean =
## 1.10, SD = 1.50) distributions. The model's explanatory power is substantial
## (R2 = 0.82, 95% CI [0.77, 0.85]) and the part related to the fixed effects
## alone (marginal R2) is of 0.80 (95% CI [0.61, 0.84]).  Within this model:
## 
##   - The effect of b Intercept (Median = 1.91, 95% CI [1.55, 2.24]) has a 100.00%
## probability of being positive (> 0), 100.00% of being significant (> 0.05), and
## 100.00% of being large (> 0.30). The estimation successfully converged (Rhat =
## 1.000) and the indices are reliable (ESS = 2331)
##   - The effect of b assessment methodfunnel (Median = -0.02, 95% CI [-0.25,
## 0.21]) has a 58.83% probability of being negative (< 0), 40.54% of being
## significant (< -0.05), and 0.92% of being large (< -0.30). The estimation
## successfully converged (Rhat = 1.002) and the indices are reliable (ESS = 2179)
##   - The effect of b assessment methodincidentals (Median = -0.91, 95% CI [-1.24,
## -0.61]) has a 100.00% probability of being negative (< 0), 100.00% of being
## significant (< -0.05), and 100.00% of being large (< -0.30). The estimation
## successfully converged (Rhat = 0.999) and the indices are reliable (ESS = 2347)
##   - The effect of b assessment methodspotlighting (Median = -1.11, 95% CI [-1.45,
## -0.78]) has a 100.00% probability of being negative (< 0), 100.00% of being
## significant (< -0.05), and 100.00% of being large (< -0.30). The estimation
## successfully converged (Rhat = 1.000) and the indices are reliable (ESS = 2200)
##   - The effect of b assessment methodcoverboard (Median = -1.57, 95% CI [-2.01,
## -1.17]) has a 100.00% probability of being negative (< 0), 100.00% of being
## significant (< -0.05), and 100.00% of being large (< -0.30). The estimation
## successfully converged (Rhat = 1.000) and the indices are reliable (ESS = 2048)
##   - The effect of b assessment methodcamera (Median = -2.48, 95% CI [-3.09,
## -1.94]) has a 100.00% probability of being negative (< 0), 100.00% of being
## significant (< -0.05), and 100.00% of being large (< -0.30). The estimation
## successfully converged (Rhat = 1.003) and the indices are reliable (ESS = 1697)
##   - The effect of b scalelatscaleEQFALSE (Median = 0.07, 95% CI [0.02, 0.12]) has
## a 99.54% probability of being positive (> 0), 84.58% of being significant (>
## 0.05), and 0.00% of being large (> 0.30). The estimation successfully converged
## (Rhat = 1.000) and the indices are reliable (ESS = 2277)
##   - The interaction effect of scalelatscaleEQFALSE on b assessment methodfunnel
## (Median = 2.43e-03, 95% CI [-0.03, 0.04]) has a 55.33% probability of being
## positive (> 0), 0.38% of being significant (> 0.05), and 0.00% of being large
## (> 0.30). The estimation successfully converged (Rhat = 1.000) and the indices
## are reliable (ESS = 2132)
##   - The interaction effect of scalelatscaleEQFALSE on b assessment
## methodincidentals (Median = 0.04, 95% CI [3.81e-04, 0.09]) has a 97.58%
## probability of being positive (> 0), 40.12% of being significant (> 0.05), and
## 0.00% of being large (> 0.30). The estimation successfully converged (Rhat =
## 1.000) and the indices are reliable (ESS = 2171)
##   - The interaction effect of scalelatscaleEQFALSE on b assessment
## methodspotlighting (Median = 0.04, 95% CI [-3.29e-03, 0.09]) has a 96.46%
## probability of being positive (> 0), 39.71% of being significant (> 0.05), and
## 0.00% of being large (> 0.30). The estimation successfully converged (Rhat =
## 0.999) and the indices are reliable (ESS = 2334)
##   - The interaction effect of scalelatscaleEQFALSE on b assessment
## methodcoverboard (Median = 0.05, 95% CI [-0.01, 0.11]) has a 94.21% probability
## of being positive (> 0), 45.88% of being significant (> 0.05), and 0.00% of
## being large (> 0.30). The estimation successfully converged (Rhat = 1.002) and
## the indices are reliable (ESS = 1302)
##   - The interaction effect of scalelatscaleEQFALSE on b assessment methodcamera
## (Median = -0.03, 95% CI [-0.11, 0.05]) has a 75.71% probability of being
## negative (< 0), 30.63% of being significant (< -0.05), and 0.00% of being large
## (< -0.30). The estimation successfully converged (Rhat = 1.001) and the indices
## are reliable (ESS = 1663)
##   - NANAThe estimation successfully converged (Rhat = 1.000) and the indices are
## reliable (ESS = 2331)
##   - NANAThe estimation successfully converged (Rhat = 1.002) and the indices are
## reliable (ESS = 2179)
##   - NANAThe estimation successfully converged (Rhat = 0.999) and the indices are
## reliable (ESS = 2347)
##   - NANAThe estimation successfully converged (Rhat = 1.000) and the indices are
## reliable (ESS = 2200)
## 
## Following the Sequential Effect eXistence and sIgnificance Testing (SEXIT)
## framework, we report the median of the posterior distribution and its 95% CI
## (Highest Density Interval), along the probability of direction (pd), the
## probability of significance and the probability of being large. The thresholds
## beyond which the effect is considered as significant (i.e., non-negligible) and
## large are |0.05| and |0.30|. Convergence and stability of the Bayesian sampling
## has been assessed using R-hat, which should be below 1.01 (Vehtari et al.,
## 2019), and Effective Sample Size (ESS), which should be greater than 1000
## (Burkner, 2017)., We fitted a Bayesian poisson mixed model (estimated using
## MCMC sampling with 3 chains of 5000 iterations and a warmup of 1000) to predict
## richness with lat (formula: richness ~ assessment.method * scale(lat, scale =
## FALSE)). The model included site.plot as random effects (formula: list(~1 |
## site.plot:site, ~1 | site)). Priors over parameters were set as normal (mean =
## 0.00, SD = 3.70) distributions. The model's explanatory power is substantial
## (R2 = 0.82, 95% CI [0.77, 0.85]) and the part related to the fixed effects
## alone (marginal R2) is of 0.80 (95% CI [0.61, 0.84]).  Within this model:
## 
##   - The effect of b Intercept (Median = 1.91, 95% CI [1.55, 2.24]) has a 100.00%
## probability of being positive (> 0), 100.00% of being significant (> 0.05), and
## 100.00% of being large (> 0.30). The estimation successfully converged (Rhat =
## 1.000) and the indices are reliable (ESS = 2331)
##   - The effect of b assessment methodfunnel (Median = -0.02, 95% CI [-0.25,
## 0.21]) has a 58.83% probability of being negative (< 0), 40.54% of being
## significant (< -0.05), and 0.92% of being large (< -0.30). The estimation
## successfully converged (Rhat = 1.002) and the indices are reliable (ESS = 2179)
##   - The effect of b assessment methodincidentals (Median = -0.91, 95% CI [-1.24,
## -0.61]) has a 100.00% probability of being negative (< 0), 100.00% of being
## significant (< -0.05), and 100.00% of being large (< -0.30). The estimation
## successfully converged (Rhat = 0.999) and the indices are reliable (ESS = 2347)
##   - The effect of b assessment methodspotlighting (Median = -1.11, 95% CI [-1.45,
## -0.78]) has a 100.00% probability of being negative (< 0), 100.00% of being
## significant (< -0.05), and 100.00% of being large (< -0.30). The estimation
## successfully converged (Rhat = 1.000) and the indices are reliable (ESS = 2200)
##   - The effect of b assessment methodcoverboard (Median = -1.57, 95% CI [-2.01,
## -1.17]) has a 100.00% probability of being negative (< 0), 100.00% of being
## significant (< -0.05), and 100.00% of being large (< -0.30). The estimation
## successfully converged (Rhat = 1.000) and the indices are reliable (ESS = 2048)
##   - The effect of b assessment methodcamera (Median = -2.48, 95% CI [-3.09,
## -1.94]) has a 100.00% probability of being negative (< 0), 100.00% of being
## significant (< -0.05), and 100.00% of being large (< -0.30). The estimation
## successfully converged (Rhat = 1.003) and the indices are reliable (ESS = 1697)
##   - The effect of b scalelatscaleEQFALSE (Median = 0.07, 95% CI [0.02, 0.12]) has
## a 99.54% probability of being positive (> 0), 84.58% of being significant (>
## 0.05), and 0.00% of being large (> 0.30). The estimation successfully converged
## (Rhat = 1.000) and the indices are reliable (ESS = 2277)
##   - The interaction effect of scalelatscaleEQFALSE on b assessment methodfunnel
## (Median = 2.43e-03, 95% CI [-0.03, 0.04]) has a 55.33% probability of being
## positive (> 0), 0.38% of being significant (> 0.05), and 0.00% of being large
## (> 0.30). The estimation successfully converged (Rhat = 1.000) and the indices
## are reliable (ESS = 2132)
##   - The interaction effect of scalelatscaleEQFALSE on b assessment
## methodincidentals (Median = 0.04, 95% CI [3.81e-04, 0.09]) has a 97.58%
## probability of being positive (> 0), 40.12% of being significant (> 0.05), and
## 0.00% of being large (> 0.30). The estimation successfully converged (Rhat =
## 1.000) and the indices are reliable (ESS = 2171)
##   - The interaction effect of scalelatscaleEQFALSE on b assessment
## methodspotlighting (Median = 0.04, 95% CI [-3.29e-03, 0.09]) has a 96.46%
## probability of being positive (> 0), 39.71% of being significant (> 0.05), and
## 0.00% of being large (> 0.30). The estimation successfully converged (Rhat =
## 0.999) and the indices are reliable (ESS = 2334)
##   - The interaction effect of scalelatscaleEQFALSE on b assessment
## methodcoverboard (Median = 0.05, 95% CI [-0.01, 0.11]) has a 94.21% probability
## of being positive (> 0), 45.88% of being significant (> 0.05), and 0.00% of
## being large (> 0.30). The estimation successfully converged (Rhat = 1.002) and
## the indices are reliable (ESS = 1302)
##   - The interaction effect of scalelatscaleEQFALSE on b assessment methodcamera
## (Median = -0.03, 95% CI [-0.11, 0.05]) has a 75.71% probability of being
## negative (< 0), 30.63% of being significant (< -0.05), and 0.00% of being large
## (< -0.30). The estimation successfully converged (Rhat = 1.001) and the indices
## are reliable (ESS = 1663)
##   - NANAThe estimation successfully converged (Rhat = 1.000) and the indices are
## reliable (ESS = 2331)
##   - NANAThe estimation successfully converged (Rhat = 1.002) and the indices are
## reliable (ESS = 2179)
##   - NANAThe estimation successfully converged (Rhat = 0.999) and the indices are
## reliable (ESS = 2347)
##   - NANAThe estimation successfully converged (Rhat = 1.000) and the indices are
## reliable (ESS = 2200)
## 
## Following the Sequential Effect eXistence and sIgnificance Testing (SEXIT)
## framework, we report the median of the posterior distribution and its 95% CI
## (Highest Density Interval), along the probability of direction (pd), the
## probability of significance and the probability of being large. The thresholds
## beyond which the effect is considered as significant (i.e., non-negligible) and
## large are |0.05| and |0.30|. Convergence and stability of the Bayesian sampling
## has been assessed using R-hat, which should be below 1.01 (Vehtari et al.,
## 2019), and Effective Sample Size (ESS), which should be greater than 1000
## (Burkner, 2017)., We fitted a Bayesian poisson mixed model (estimated using
## MCMC sampling with 3 chains of 5000 iterations and a warmup of 1000) to predict
## richness with assessment.method (formula: richness ~ assessment.method *
## scale(lat, scale = FALSE)). The model included site.plot as random effects
## (formula: list(~1 | site.plot:site, ~1 | site)). Priors over parameters were
## set as normal (mean = 0.00, SD = 3.70) distributions. The model's explanatory
## power is substantial (R2 = 0.82, 95% CI [0.77, 0.85]) and the part related to
## the fixed effects alone (marginal R2) is of 0.80 (95% CI [0.61, 0.84]).  Within
## this model:
## 
##   - The effect of b Intercept (Median = 1.91, 95% CI [1.55, 2.24]) has a 100.00%
## probability of being positive (> 0), 100.00% of being significant (> 0.05), and
## 100.00% of being large (> 0.30). The estimation successfully converged (Rhat =
## 1.000) and the indices are reliable (ESS = 2331)
##   - The effect of b assessment methodfunnel (Median = -0.02, 95% CI [-0.25,
## 0.21]) has a 58.83% probability of being negative (< 0), 40.54% of being
## significant (< -0.05), and 0.92% of being large (< -0.30). The estimation
## successfully converged (Rhat = 1.002) and the indices are reliable (ESS = 2179)
##   - The effect of b assessment methodincidentals (Median = -0.91, 95% CI [-1.24,
## -0.61]) has a 100.00% probability of being negative (< 0), 100.00% of being
## significant (< -0.05), and 100.00% of being large (< -0.30). The estimation
## successfully converged (Rhat = 0.999) and the indices are reliable (ESS = 2347)
##   - The effect of b assessment methodspotlighting (Median = -1.11, 95% CI [-1.45,
## -0.78]) has a 100.00% probability of being negative (< 0), 100.00% of being
## significant (< -0.05), and 100.00% of being large (< -0.30). The estimation
## successfully converged (Rhat = 1.000) and the indices are reliable (ESS = 2200)
##   - The effect of b assessment methodcoverboard (Median = -1.57, 95% CI [-2.01,
## -1.17]) has a 100.00% probability of being negative (< 0), 100.00% of being
## significant (< -0.05), and 100.00% of being large (< -0.30). The estimation
## successfully converged (Rhat = 1.000) and the indices are reliable (ESS = 2048)
##   - The effect of b assessment methodcamera (Median = -2.48, 95% CI [-3.09,
## -1.94]) has a 100.00% probability of being negative (< 0), 100.00% of being
## significant (< -0.05), and 100.00% of being large (< -0.30). The estimation
## successfully converged (Rhat = 1.003) and the indices are reliable (ESS = 1697)
##   - The effect of b scalelatscaleEQFALSE (Median = 0.07, 95% CI [0.02, 0.12]) has
## a 99.54% probability of being positive (> 0), 84.58% of being significant (>
## 0.05), and 0.00% of being large (> 0.30). The estimation successfully converged
## (Rhat = 1.000) and the indices are reliable (ESS = 2277)
##   - The interaction effect of scalelatscaleEQFALSE on b assessment methodfunnel
## (Median = 2.43e-03, 95% CI [-0.03, 0.04]) has a 55.33% probability of being
## positive (> 0), 0.38% of being significant (> 0.05), and 0.00% of being large
## (> 0.30). The estimation successfully converged (Rhat = 1.000) and the indices
## are reliable (ESS = 2132)
##   - The interaction effect of scalelatscaleEQFALSE on b assessment
## methodincidentals (Median = 0.04, 95% CI [3.81e-04, 0.09]) has a 97.58%
## probability of being positive (> 0), 40.12% of being significant (> 0.05), and
## 0.00% of being large (> 0.30). The estimation successfully converged (Rhat =
## 1.000) and the indices are reliable (ESS = 2171)
##   - The interaction effect of scalelatscaleEQFALSE on b assessment
## methodspotlighting (Median = 0.04, 95% CI [-3.29e-03, 0.09]) has a 96.46%
## probability of being positive (> 0), 39.71% of being significant (> 0.05), and
## 0.00% of being large (> 0.30). The estimation successfully converged (Rhat =
## 0.999) and the indices are reliable (ESS = 2334)
##   - The interaction effect of scalelatscaleEQFALSE on b assessment
## methodcoverboard (Median = 0.05, 95% CI [-0.01, 0.11]) has a 94.21% probability
## of being positive (> 0), 45.88% of being significant (> 0.05), and 0.00% of
## being large (> 0.30). The estimation successfully converged (Rhat = 1.002) and
## the indices are reliable (ESS = 1302)
##   - The interaction effect of scalelatscaleEQFALSE on b assessment methodcamera
## (Median = -0.03, 95% CI [-0.11, 0.05]) has a 75.71% probability of being
## negative (< 0), 30.63% of being significant (< -0.05), and 0.00% of being large
## (< -0.30). The estimation successfully converged (Rhat = 1.001) and the indices
## are reliable (ESS = 1663)
##   - NANAThe estimation successfully converged (Rhat = 1.000) and the indices are
## reliable (ESS = 2331)
##   - NANAThe estimation successfully converged (Rhat = 1.002) and the indices are
## reliable (ESS = 2179)
##   - NANAThe estimation successfully converged (Rhat = 0.999) and the indices are
## reliable (ESS = 2347)
##   - NANAThe estimation successfully converged (Rhat = 1.000) and the indices are
## reliable (ESS = 2200)
## 
## Following the Sequential Effect eXistence and sIgnificance Testing (SEXIT)
## framework, we report the median of the posterior distribution and its 95% CI
## (Highest Density Interval), along the probability of direction (pd), the
## probability of significance and the probability of being large. The thresholds
## beyond which the effect is considered as significant (i.e., non-negligible) and
## large are |0.05| and |0.30|. Convergence and stability of the Bayesian sampling
## has been assessed using R-hat, which should be below 1.01 (Vehtari et al.,
## 2019), and Effective Sample Size (ESS), which should be greater than 1000
## (Burkner, 2017)., We fitted a Bayesian poisson mixed model (estimated using
## MCMC sampling with 3 chains of 5000 iterations and a warmup of 1000) to predict
## richness with lat (formula: richness ~ assessment.method * scale(lat, scale =
## FALSE)). The model included site.plot as random effects (formula: list(~1 |
## site.plot:site, ~1 | site)). Priors over parameters were set as normal (mean =
## 0.00, SD = 3.70) distributions. The model's explanatory power is substantial
## (R2 = 0.82, 95% CI [0.77, 0.85]) and the part related to the fixed effects
## alone (marginal R2) is of 0.80 (95% CI [0.61, 0.84]).  Within this model:
## 
##   - The effect of b Intercept (Median = 1.91, 95% CI [1.55, 2.24]) has a 100.00%
## probability of being positive (> 0), 100.00% of being significant (> 0.05), and
## 100.00% of being large (> 0.30). The estimation successfully converged (Rhat =
## 1.000) and the indices are reliable (ESS = 2331)
##   - The effect of b assessment methodfunnel (Median = -0.02, 95% CI [-0.25,
## 0.21]) has a 58.83% probability of being negative (< 0), 40.54% of being
## significant (< -0.05), and 0.92% of being large (< -0.30). The estimation
## successfully converged (Rhat = 1.002) and the indices are reliable (ESS = 2179)
##   - The effect of b assessment methodincidentals (Median = -0.91, 95% CI [-1.24,
## -0.61]) has a 100.00% probability of being negative (< 0), 100.00% of being
## significant (< -0.05), and 100.00% of being large (< -0.30). The estimation
## successfully converged (Rhat = 0.999) and the indices are reliable (ESS = 2347)
##   - The effect of b assessment methodspotlighting (Median = -1.11, 95% CI [-1.45,
## -0.78]) has a 100.00% probability of being negative (< 0), 100.00% of being
## significant (< -0.05), and 100.00% of being large (< -0.30). The estimation
## successfully converged (Rhat = 1.000) and the indices are reliable (ESS = 2200)
##   - The effect of b assessment methodcoverboard (Median = -1.57, 95% CI [-2.01,
## -1.17]) has a 100.00% probability of being negative (< 0), 100.00% of being
## significant (< -0.05), and 100.00% of being large (< -0.30). The estimation
## successfully converged (Rhat = 1.000) and the indices are reliable (ESS = 2048)
##   - The effect of b assessment methodcamera (Median = -2.48, 95% CI [-3.09,
## -1.94]) has a 100.00% probability of being negative (< 0), 100.00% of being
## significant (< -0.05), and 100.00% of being large (< -0.30). The estimation
## successfully converged (Rhat = 1.003) and the indices are reliable (ESS = 1697)
##   - The effect of b scalelatscaleEQFALSE (Median = 0.07, 95% CI [0.02, 0.12]) has
## a 99.54% probability of being positive (> 0), 84.58% of being significant (>
## 0.05), and 0.00% of being large (> 0.30). The estimation successfully converged
## (Rhat = 1.000) and the indices are reliable (ESS = 2277)
##   - The interaction effect of scalelatscaleEQFALSE on b assessment methodfunnel
## (Median = 2.43e-03, 95% CI [-0.03, 0.04]) has a 55.33% probability of being
## positive (> 0), 0.38% of being significant (> 0.05), and 0.00% of being large
## (> 0.30). The estimation successfully converged (Rhat = 1.000) and the indices
## are reliable (ESS = 2132)
##   - The interaction effect of scalelatscaleEQFALSE on b assessment
## methodincidentals (Median = 0.04, 95% CI [3.81e-04, 0.09]) has a 97.58%
## probability of being positive (> 0), 40.12% of being significant (> 0.05), and
## 0.00% of being large (> 0.30). The estimation successfully converged (Rhat =
## 1.000) and the indices are reliable (ESS = 2171)
##   - The interaction effect of scalelatscaleEQFALSE on b assessment
## methodspotlighting (Median = 0.04, 95% CI [-3.29e-03, 0.09]) has a 96.46%
## probability of being positive (> 0), 39.71% of being significant (> 0.05), and
## 0.00% of being large (> 0.30). The estimation successfully converged (Rhat =
## 0.999) and the indices are reliable (ESS = 2334)
##   - The interaction effect of scalelatscaleEQFALSE on b assessment
## methodcoverboard (Median = 0.05, 95% CI [-0.01, 0.11]) has a 94.21% probability
## of being positive (> 0), 45.88% of being significant (> 0.05), and 0.00% of
## being large (> 0.30). The estimation successfully converged (Rhat = 1.002) and
## the indices are reliable (ESS = 1302)
##   - The interaction effect of scalelatscaleEQFALSE on b assessment methodcamera
## (Median = -0.03, 95% CI [-0.11, 0.05]) has a 75.71% probability of being
## negative (< 0), 30.63% of being significant (< -0.05), and 0.00% of being large
## (< -0.30). The estimation successfully converged (Rhat = 1.001) and the indices
## are reliable (ESS = 1663)
##   - NANAThe estimation successfully converged (Rhat = 1.000) and the indices are
## reliable (ESS = 2331)
##   - NANAThe estimation successfully converged (Rhat = 1.002) and the indices are
## reliable (ESS = 2179)
##   - NANAThe estimation successfully converged (Rhat = 0.999) and the indices are
## reliable (ESS = 2347)
##   - NANAThe estimation successfully converged (Rhat = 1.000) and the indices are
## reliable (ESS = 2200)
## 
## Following the Sequential Effect eXistence and sIgnificance Testing (SEXIT)
## framework, we report the median of the posterior distribution and its 95% CI
## (Highest Density Interval), along the probability of direction (pd), the
## probability of significance and the probability of being large. The thresholds
## beyond which the effect is considered as significant (i.e., non-negligible) and
## large are |0.05| and |0.30|. Convergence and stability of the Bayesian sampling
## has been assessed using R-hat, which should be below 1.01 (Vehtari et al.,
## 2019), and Effective Sample Size (ESS), which should be greater than 1000
## (Burkner, 2017)., We fitted a Bayesian poisson mixed model (estimated using
## MCMC sampling with 3 chains of 5000 iterations and a warmup of 1000) to predict
## richness with assessment.method (formula: richness ~ assessment.method *
## scale(lat, scale = FALSE)). The model included site.plot as random effects
## (formula: list(~1 | site.plot:site, ~1 | site)). Priors over parameters were
## set as normal (mean = 0.00, SD = 3.70) distributions. The model's explanatory
## power is substantial (R2 = 0.82, 95% CI [0.77, 0.85]) and the part related to
## the fixed effects alone (marginal R2) is of 0.80 (95% CI [0.61, 0.84]).  Within
## this model:
## 
##   - The effect of b Intercept (Median = 1.91, 95% CI [1.55, 2.24]) has a 100.00%
## probability of being positive (> 0), 100.00% of being significant (> 0.05), and
## 100.00% of being large (> 0.30). The estimation successfully converged (Rhat =
## 1.000) and the indices are reliable (ESS = 2331)
##   - The effect of b assessment methodfunnel (Median = -0.02, 95% CI [-0.25,
## 0.21]) has a 58.83% probability of being negative (< 0), 40.54% of being
## significant (< -0.05), and 0.92% of being large (< -0.30). The estimation
## successfully converged (Rhat = 1.002) and the indices are reliable (ESS = 2179)
##   - The effect of b assessment methodincidentals (Median = -0.91, 95% CI [-1.24,
## -0.61]) has a 100.00% probability of being negative (< 0), 100.00% of being
## significant (< -0.05), and 100.00% of being large (< -0.30). The estimation
## successfully converged (Rhat = 0.999) and the indices are reliable (ESS = 2347)
##   - The effect of b assessment methodspotlighting (Median = -1.11, 95% CI [-1.45,
## -0.78]) has a 100.00% probability of being negative (< 0), 100.00% of being
## significant (< -0.05), and 100.00% of being large (< -0.30). The estimation
## successfully converged (Rhat = 1.000) and the indices are reliable (ESS = 2200)
##   - The effect of b assessment methodcoverboard (Median = -1.57, 95% CI [-2.01,
## -1.17]) has a 100.00% probability of being negative (< 0), 100.00% of being
## significant (< -0.05), and 100.00% of being large (< -0.30). The estimation
## successfully converged (Rhat = 1.000) and the indices are reliable (ESS = 2048)
##   - The effect of b assessment methodcamera (Median = -2.48, 95% CI [-3.09,
## -1.94]) has a 100.00% probability of being negative (< 0), 100.00% of being
## significant (< -0.05), and 100.00% of being large (< -0.30). The estimation
## successfully converged (Rhat = 1.003) and the indices are reliable (ESS = 1697)
##   - The effect of b scalelatscaleEQFALSE (Median = 0.07, 95% CI [0.02, 0.12]) has
## a 99.54% probability of being positive (> 0), 84.58% of being significant (>
## 0.05), and 0.00% of being large (> 0.30). The estimation successfully converged
## (Rhat = 1.000) and the indices are reliable (ESS = 2277)
##   - The interaction effect of scalelatscaleEQFALSE on b assessment methodfunnel
## (Median = 2.43e-03, 95% CI [-0.03, 0.04]) has a 55.33% probability of being
## positive (> 0), 0.38% of being significant (> 0.05), and 0.00% of being large
## (> 0.30). The estimation successfully converged (Rhat = 1.000) and the indices
## are reliable (ESS = 2132)
##   - The interaction effect of scalelatscaleEQFALSE on b assessment
## methodincidentals (Median = 0.04, 95% CI [3.81e-04, 0.09]) has a 97.58%
## probability of being positive (> 0), 40.12% of being significant (> 0.05), and
## 0.00% of being large (> 0.30). The estimation successfully converged (Rhat =
## 1.000) and the indices are reliable (ESS = 2171)
##   - The interaction effect of scalelatscaleEQFALSE on b assessment
## methodspotlighting (Median = 0.04, 95% CI [-3.29e-03, 0.09]) has a 96.46%
## probability of being positive (> 0), 39.71% of being significant (> 0.05), and
## 0.00% of being large (> 0.30). The estimation successfully converged (Rhat =
## 0.999) and the indices are reliable (ESS = 2334)
##   - The interaction effect of scalelatscaleEQFALSE on b assessment
## methodcoverboard (Median = 0.05, 95% CI [-0.01, 0.11]) has a 94.21% probability
## of being positive (> 0), 45.88% of being significant (> 0.05), and 0.00% of
## being large (> 0.30). The estimation successfully converged (Rhat = 1.002) and
## the indices are reliable (ESS = 1302)
##   - The interaction effect of scalelatscaleEQFALSE on b assessment methodcamera
## (Median = -0.03, 95% CI [-0.11, 0.05]) has a 75.71% probability of being
## negative (< 0), 30.63% of being significant (< -0.05), and 0.00% of being large
## (< -0.30). The estimation successfully converged (Rhat = 1.001) and the indices
## are reliable (ESS = 1663)
##   - NANAThe estimation successfully converged (Rhat = 1.000) and the indices are
## reliable (ESS = 2331)
##   - NANAThe estimation successfully converged (Rhat = 1.002) and the indices are
## reliable (ESS = 2179)
##   - NANAThe estimation successfully converged (Rhat = 0.999) and the indices are
## reliable (ESS = 2347)
##   - NANAThe estimation successfully converged (Rhat = 1.000) and the indices are
## reliable (ESS = 2200)
## 
## Following the Sequential Effect eXistence and sIgnificance Testing (SEXIT)
## framework, we report the median of the posterior distribution and its 95% CI
## (Highest Density Interval), along the probability of direction (pd), the
## probability of significance and the probability of being large. The thresholds
## beyond which the effect is considered as significant (i.e., non-negligible) and
## large are |0.05| and |0.30|. Convergence and stability of the Bayesian sampling
## has been assessed using R-hat, which should be below 1.01 (Vehtari et al.,
## 2019), and Effective Sample Size (ESS), which should be greater than 1000
## (Burkner, 2017)., We fitted a Bayesian poisson mixed model (estimated using
## MCMC sampling with 3 chains of 5000 iterations and a warmup of 1000) to predict
## richness with lat (formula: richness ~ assessment.method * scale(lat, scale =
## FALSE)). The model included site.plot as random effects (formula: list(~1 |
## site.plot:site, ~1 | site)). Priors over parameters were set as normal (mean =
## 0.00, SD = 3.70) distributions. The model's explanatory power is substantial
## (R2 = 0.82, 95% CI [0.77, 0.85]) and the part related to the fixed effects
## alone (marginal R2) is of 0.80 (95% CI [0.61, 0.84]).  Within this model:
## 
##   - The effect of b Intercept (Median = 1.91, 95% CI [1.55, 2.24]) has a 100.00%
## probability of being positive (> 0), 100.00% of being significant (> 0.05), and
## 100.00% of being large (> 0.30). The estimation successfully converged (Rhat =
## 1.000) and the indices are reliable (ESS = 2331)
##   - The effect of b assessment methodfunnel (Median = -0.02, 95% CI [-0.25,
## 0.21]) has a 58.83% probability of being negative (< 0), 40.54% of being
## significant (< -0.05), and 0.92% of being large (< -0.30). The estimation
## successfully converged (Rhat = 1.002) and the indices are reliable (ESS = 2179)
##   - The effect of b assessment methodincidentals (Median = -0.91, 95% CI [-1.24,
## -0.61]) has a 100.00% probability of being negative (< 0), 100.00% of being
## significant (< -0.05), and 100.00% of being large (< -0.30). The estimation
## successfully converged (Rhat = 0.999) and the indices are reliable (ESS = 2347)
##   - The effect of b assessment methodspotlighting (Median = -1.11, 95% CI [-1.45,
## -0.78]) has a 100.00% probability of being negative (< 0), 100.00% of being
## significant (< -0.05), and 100.00% of being large (< -0.30). The estimation
## successfully converged (Rhat = 1.000) and the indices are reliable (ESS = 2200)
##   - The effect of b assessment methodcoverboard (Median = -1.57, 95% CI [-2.01,
## -1.17]) has a 100.00% probability of being negative (< 0), 100.00% of being
## significant (< -0.05), and 100.00% of being large (< -0.30). The estimation
## successfully converged (Rhat = 1.000) and the indices are reliable (ESS = 2048)
##   - The effect of b assessment methodcamera (Median = -2.48, 95% CI [-3.09,
## -1.94]) has a 100.00% probability of being negative (< 0), 100.00% of being
## significant (< -0.05), and 100.00% of being large (< -0.30). The estimation
## successfully converged (Rhat = 1.003) and the indices are reliable (ESS = 1697)
##   - The effect of b scalelatscaleEQFALSE (Median = 0.07, 95% CI [0.02, 0.12]) has
## a 99.54% probability of being positive (> 0), 84.58% of being significant (>
## 0.05), and 0.00% of being large (> 0.30). The estimation successfully converged
## (Rhat = 1.000) and the indices are reliable (ESS = 2277)
##   - The interaction effect of scalelatscaleEQFALSE on b assessment methodfunnel
## (Median = 2.43e-03, 95% CI [-0.03, 0.04]) has a 55.33% probability of being
## positive (> 0), 0.38% of being significant (> 0.05), and 0.00% of being large
## (> 0.30). The estimation successfully converged (Rhat = 1.000) and the indices
## are reliable (ESS = 2132)
##   - The interaction effect of scalelatscaleEQFALSE on b assessment
## methodincidentals (Median = 0.04, 95% CI [3.81e-04, 0.09]) has a 97.58%
## probability of being positive (> 0), 40.12% of being significant (> 0.05), and
## 0.00% of being large (> 0.30). The estimation successfully converged (Rhat =
## 1.000) and the indices are reliable (ESS = 2171)
##   - The interaction effect of scalelatscaleEQFALSE on b assessment
## methodspotlighting (Median = 0.04, 95% CI [-3.29e-03, 0.09]) has a 96.46%
## probability of being positive (> 0), 39.71% of being significant (> 0.05), and
## 0.00% of being large (> 0.30). The estimation successfully converged (Rhat =
## 0.999) and the indices are reliable (ESS = 2334)
##   - The interaction effect of scalelatscaleEQFALSE on b assessment
## methodcoverboard (Median = 0.05, 95% CI [-0.01, 0.11]) has a 94.21% probability
## of being positive (> 0), 45.88% of being significant (> 0.05), and 0.00% of
## being large (> 0.30). The estimation successfully converged (Rhat = 1.002) and
## the indices are reliable (ESS = 1302)
##   - The interaction effect of scalelatscaleEQFALSE on b assessment methodcamera
## (Median = -0.03, 95% CI [-0.11, 0.05]) has a 75.71% probability of being
## negative (< 0), 30.63% of being significant (< -0.05), and 0.00% of being large
## (< -0.30). The estimation successfully converged (Rhat = 1.001) and the indices
## are reliable (ESS = 1663)
##   - NANAThe estimation successfully converged (Rhat = 1.000) and the indices are
## reliable (ESS = 2331)
##   - NANAThe estimation successfully converged (Rhat = 1.002) and the indices are
## reliable (ESS = 2179)
##   - NANAThe estimation successfully converged (Rhat = 0.999) and the indices are
## reliable (ESS = 2347)
##   - NANAThe estimation successfully converged (Rhat = 1.000) and the indices are
## reliable (ESS = 2200)
## 
## Following the Sequential Effect eXistence and sIgnificance Testing (SEXIT)
## framework, we report the median of the posterior distribution and its 95% CI
## (Highest Density Interval), along the probability of direction (pd), the
## probability of significance and the probability of being large. The thresholds
## beyond which the effect is considered as significant (i.e., non-negligible) and
## large are |0.05| and |0.30|. Convergence and stability of the Bayesian sampling
## has been assessed using R-hat, which should be below 1.01 (Vehtari et al.,
## 2019), and Effective Sample Size (ESS), which should be greater than 1000
## (Burkner, 2017)., We fitted a Bayesian poisson mixed model (estimated using
## MCMC sampling with 3 chains of 5000 iterations and a warmup of 1000) to predict
## richness with assessment.method (formula: richness ~ assessment.method *
## scale(lat, scale = FALSE)). The model included site.plot as random effects
## (formula: list(~1 | site.plot:site, ~1 | site)). Priors over parameters were
## set as normal (mean = 0.00, SD = 3.70) distributions. The model's explanatory
## power is substantial (R2 = 0.82, 95% CI [0.77, 0.85]) and the part related to
## the fixed effects alone (marginal R2) is of 0.80 (95% CI [0.61, 0.84]).  Within
## this model:
## 
##   - The effect of b Intercept (Median = 1.91, 95% CI [1.55, 2.24]) has a 100.00%
## probability of being positive (> 0), 100.00% of being significant (> 0.05), and
## 100.00% of being large (> 0.30). The estimation successfully converged (Rhat =
## 1.000) and the indices are reliable (ESS = 2331)
##   - The effect of b assessment methodfunnel (Median = -0.02, 95% CI [-0.25,
## 0.21]) has a 58.83% probability of being negative (< 0), 40.54% of being
## significant (< -0.05), and 0.92% of being large (< -0.30). The estimation
## successfully converged (Rhat = 1.002) and the indices are reliable (ESS = 2179)
##   - The effect of b assessment methodincidentals (Median = -0.91, 95% CI [-1.24,
## -0.61]) has a 100.00% probability of being negative (< 0), 100.00% of being
## significant (< -0.05), and 100.00% of being large (< -0.30). The estimation
## successfully converged (Rhat = 0.999) and the indices are reliable (ESS = 2347)
##   - The effect of b assessment methodspotlighting (Median = -1.11, 95% CI [-1.45,
## -0.78]) has a 100.00% probability of being negative (< 0), 100.00% of being
## significant (< -0.05), and 100.00% of being large (< -0.30). The estimation
## successfully converged (Rhat = 1.000) and the indices are reliable (ESS = 2200)
##   - The effect of b assessment methodcoverboard (Median = -1.57, 95% CI [-2.01,
## -1.17]) has a 100.00% probability of being negative (< 0), 100.00% of being
## significant (< -0.05), and 100.00% of being large (< -0.30). The estimation
## successfully converged (Rhat = 1.000) and the indices are reliable (ESS = 2048)
##   - The effect of b assessment methodcamera (Median = -2.48, 95% CI [-3.09,
## -1.94]) has a 100.00% probability of being negative (< 0), 100.00% of being
## significant (< -0.05), and 100.00% of being large (< -0.30). The estimation
## successfully converged (Rhat = 1.003) and the indices are reliable (ESS = 1697)
##   - The effect of b scalelatscaleEQFALSE (Median = 0.07, 95% CI [0.02, 0.12]) has
## a 99.54% probability of being positive (> 0), 84.58% of being significant (>
## 0.05), and 0.00% of being large (> 0.30). The estimation successfully converged
## (Rhat = 1.000) and the indices are reliable (ESS = 2277)
##   - The interaction effect of scalelatscaleEQFALSE on b assessment methodfunnel
## (Median = 2.43e-03, 95% CI [-0.03, 0.04]) has a 55.33% probability of being
## positive (> 0), 0.38% of being significant (> 0.05), and 0.00% of being large
## (> 0.30). The estimation successfully converged (Rhat = 1.000) and the indices
## are reliable (ESS = 2132)
##   - The interaction effect of scalelatscaleEQFALSE on b assessment
## methodincidentals (Median = 0.04, 95% CI [3.81e-04, 0.09]) has a 97.58%
## probability of being positive (> 0), 40.12% of being significant (> 0.05), and
## 0.00% of being large (> 0.30). The estimation successfully converged (Rhat =
## 1.000) and the indices are reliable (ESS = 2171)
##   - The interaction effect of scalelatscaleEQFALSE on b assessment
## methodspotlighting (Median = 0.04, 95% CI [-3.29e-03, 0.09]) has a 96.46%
## probability of being positive (> 0), 39.71% of being significant (> 0.05), and
## 0.00% of being large (> 0.30). The estimation successfully converged (Rhat =
## 0.999) and the indices are reliable (ESS = 2334)
##   - The interaction effect of scalelatscaleEQFALSE on b assessment
## methodcoverboard (Median = 0.05, 95% CI [-0.01, 0.11]) has a 94.21% probability
## of being positive (> 0), 45.88% of being significant (> 0.05), and 0.00% of
## being large (> 0.30). The estimation successfully converged (Rhat = 1.002) and
## the indices are reliable (ESS = 1302)
##   - The interaction effect of scalelatscaleEQFALSE on b assessment methodcamera
## (Median = -0.03, 95% CI [-0.11, 0.05]) has a 75.71% probability of being
## negative (< 0), 30.63% of being significant (< -0.05), and 0.00% of being large
## (< -0.30). The estimation successfully converged (Rhat = 1.001) and the indices
## are reliable (ESS = 1663)
##   - NANAThe estimation successfully converged (Rhat = 1.000) and the indices are
## reliable (ESS = 2331)
##   - NANAThe estimation successfully converged (Rhat = 1.002) and the indices are
## reliable (ESS = 2179)
##   - NANAThe estimation successfully converged (Rhat = 0.999) and the indices are
## reliable (ESS = 2347)
##   - NANAThe estimation successfully converged (Rhat = 1.000) and the indices are
## reliable (ESS = 2200)
## 
## Following the Sequential Effect eXistence and sIgnificance Testing (SEXIT)
## framework, we report the median of the posterior distribution and its 95% CI
## (Highest Density Interval), along the probability of direction (pd), the
## probability of significance and the probability of being large. The thresholds
## beyond which the effect is considered as significant (i.e., non-negligible) and
## large are |0.05| and |0.30|. Convergence and stability of the Bayesian sampling
## has been assessed using R-hat, which should be below 1.01 (Vehtari et al.,
## 2019), and Effective Sample Size (ESS), which should be greater than 1000
## (Burkner, 2017)., We fitted a Bayesian poisson mixed model (estimated using
## MCMC sampling with 3 chains of 5000 iterations and a warmup of 1000) to predict
## richness with lat (formula: richness ~ assessment.method * scale(lat, scale =
## FALSE)). The model included site.plot as random effects (formula: list(~1 |
## site.plot:site, ~1 | site)). Priors over parameters were set as normal (mean =
## 0.00, SD = 3.70) distributions. The model's explanatory power is substantial
## (R2 = 0.82, 95% CI [0.77, 0.85]) and the part related to the fixed effects
## alone (marginal R2) is of 0.80 (95% CI [0.61, 0.84]).  Within this model:
## 
##   - The effect of b Intercept (Median = 1.91, 95% CI [1.55, 2.24]) has a 100.00%
## probability of being positive (> 0), 100.00% of being significant (> 0.05), and
## 100.00% of being large (> 0.30). The estimation successfully converged (Rhat =
## 1.000) and the indices are reliable (ESS = 2331)
##   - The effect of b assessment methodfunnel (Median = -0.02, 95% CI [-0.25,
## 0.21]) has a 58.83% probability of being negative (< 0), 40.54% of being
## significant (< -0.05), and 0.92% of being large (< -0.30). The estimation
## successfully converged (Rhat = 1.002) and the indices are reliable (ESS = 2179)
##   - The effect of b assessment methodincidentals (Median = -0.91, 95% CI [-1.24,
## -0.61]) has a 100.00% probability of being negative (< 0), 100.00% of being
## significant (< -0.05), and 100.00% of being large (< -0.30). The estimation
## successfully converged (Rhat = 0.999) and the indices are reliable (ESS = 2347)
##   - The effect of b assessment methodspotlighting (Median = -1.11, 95% CI [-1.45,
## -0.78]) has a 100.00% probability of being negative (< 0), 100.00% of being
## significant (< -0.05), and 100.00% of being large (< -0.30). The estimation
## successfully converged (Rhat = 1.000) and the indices are reliable (ESS = 2200)
##   - The effect of b assessment methodcoverboard (Median = -1.57, 95% CI [-2.01,
## -1.17]) has a 100.00% probability of being negative (< 0), 100.00% of being
## significant (< -0.05), and 100.00% of being large (< -0.30). The estimation
## successfully converged (Rhat = 1.000) and the indices are reliable (ESS = 2048)
##   - The effect of b assessment methodcamera (Median = -2.48, 95% CI [-3.09,
## -1.94]) has a 100.00% probability of being negative (< 0), 100.00% of being
## significant (< -0.05), and 100.00% of being large (< -0.30). The estimation
## successfully converged (Rhat = 1.003) and the indices are reliable (ESS = 1697)
##   - The effect of b scalelatscaleEQFALSE (Median = 0.07, 95% CI [0.02, 0.12]) has
## a 99.54% probability of being positive (> 0), 84.58% of being significant (>
## 0.05), and 0.00% of being large (> 0.30). The estimation successfully converged
## (Rhat = 1.000) and the indices are reliable (ESS = 2277)
##   - The interaction effect of scalelatscaleEQFALSE on b assessment methodfunnel
## (Median = 2.43e-03, 95% CI [-0.03, 0.04]) has a 55.33% probability of being
## positive (> 0), 0.38% of being significant (> 0.05), and 0.00% of being large
## (> 0.30). The estimation successfully converged (Rhat = 1.000) and the indices
## are reliable (ESS = 2132)
##   - The interaction effect of scalelatscaleEQFALSE on b assessment
## methodincidentals (Median = 0.04, 95% CI [3.81e-04, 0.09]) has a 97.58%
## probability of being positive (> 0), 40.12% of being significant (> 0.05), and
## 0.00% of being large (> 0.30). The estimation successfully converged (Rhat =
## 1.000) and the indices are reliable (ESS = 2171)
##   - The interaction effect of scalelatscaleEQFALSE on b assessment
## methodspotlighting (Median = 0.04, 95% CI [-3.29e-03, 0.09]) has a 96.46%
## probability of being positive (> 0), 39.71% of being significant (> 0.05), and
## 0.00% of being large (> 0.30). The estimation successfully converged (Rhat =
## 0.999) and the indices are reliable (ESS = 2334)
##   - The interaction effect of scalelatscaleEQFALSE on b assessment
## methodcoverboard (Median = 0.05, 95% CI [-0.01, 0.11]) has a 94.21% probability
## of being positive (> 0), 45.88% of being significant (> 0.05), and 0.00% of
## being large (> 0.30). The estimation successfully converged (Rhat = 1.002) and
## the indices are reliable (ESS = 1302)
##   - The interaction effect of scalelatscaleEQFALSE on b assessment methodcamera
## (Median = -0.03, 95% CI [-0.11, 0.05]) has a 75.71% probability of being
## negative (< 0), 30.63% of being significant (< -0.05), and 0.00% of being large
## (< -0.30). The estimation successfully converged (Rhat = 1.001) and the indices
## are reliable (ESS = 1663)
##   - NANAThe estimation successfully converged (Rhat = 1.000) and the indices are
## reliable (ESS = 2331)
##   - NANAThe estimation successfully converged (Rhat = 1.002) and the indices are
## reliable (ESS = 2179)
##   - NANAThe estimation successfully converged (Rhat = 0.999) and the indices are
## reliable (ESS = 2347)
##   - NANAThe estimation successfully converged (Rhat = 1.000) and the indices are
## reliable (ESS = 2200)
## 
## Following the Sequential Effect eXistence and sIgnificance Testing (SEXIT)
## framework, we report the median of the posterior distribution and its 95% CI
## (Highest Density Interval), along the probability of direction (pd), the
## probability of significance and the probability of being large. The thresholds
## beyond which the effect is considered as significant (i.e., non-negligible) and
## large are |0.05| and |0.30|. Convergence and stability of the Bayesian sampling
## has been assessed using R-hat, which should be below 1.01 (Vehtari et al.,
## 2019), and Effective Sample Size (ESS), which should be greater than 1000
## (Burkner, 2017)., We fitted a Bayesian poisson mixed model (estimated using
## MCMC sampling with 3 chains of 5000 iterations and a warmup of 1000) to predict
## richness with assessment.method (formula: richness ~ assessment.method *
## scale(lat, scale = FALSE)). The model included site.plot as random effects
## (formula: list(~1 | site.plot:site, ~1 | site)). Priors over parameters were
## set as normal (mean = 0.00, SD = 3.70) distributions. The model's explanatory
## power is substantial (R2 = 0.82, 95% CI [0.77, 0.85]) and the part related to
## the fixed effects alone (marginal R2) is of 0.80 (95% CI [0.61, 0.84]).  Within
## this model:
## 
##   - The effect of b Intercept (Median = 1.91, 95% CI [1.55, 2.24]) has a 100.00%
## probability of being positive (> 0), 100.00% of being significant (> 0.05), and
## 100.00% of being large (> 0.30). The estimation successfully converged (Rhat =
## 1.000) and the indices are reliable (ESS = 2331)
##   - The effect of b assessment methodfunnel (Median = -0.02, 95% CI [-0.25,
## 0.21]) has a 58.83% probability of being negative (< 0), 40.54% of being
## significant (< -0.05), and 0.92% of being large (< -0.30). The estimation
## successfully converged (Rhat = 1.002) and the indices are reliable (ESS = 2179)
##   - The effect of b assessment methodincidentals (Median = -0.91, 95% CI [-1.24,
## -0.61]) has a 100.00% probability of being negative (< 0), 100.00% of being
## significant (< -0.05), and 100.00% of being large (< -0.30). The estimation
## successfully converged (Rhat = 0.999) and the indices are reliable (ESS = 2347)
##   - The effect of b assessment methodspotlighting (Median = -1.11, 95% CI [-1.45,
## -0.78]) has a 100.00% probability of being negative (< 0), 100.00% of being
## significant (< -0.05), and 100.00% of being large (< -0.30). The estimation
## successfully converged (Rhat = 1.000) and the indices are reliable (ESS = 2200)
##   - The effect of b assessment methodcoverboard (Median = -1.57, 95% CI [-2.01,
## -1.17]) has a 100.00% probability of being negative (< 0), 100.00% of being
## significant (< -0.05), and 100.00% of being large (< -0.30). The estimation
## successfully converged (Rhat = 1.000) and the indices are reliable (ESS = 2048)
##   - The effect of b assessment methodcamera (Median = -2.48, 95% CI [-3.09,
## -1.94]) has a 100.00% probability of being negative (< 0), 100.00% of being
## significant (< -0.05), and 100.00% of being large (< -0.30). The estimation
## successfully converged (Rhat = 1.003) and the indices are reliable (ESS = 1697)
##   - The effect of b scalelatscaleEQFALSE (Median = 0.07, 95% CI [0.02, 0.12]) has
## a 99.54% probability of being positive (> 0), 84.58% of being significant (>
## 0.05), and 0.00% of being large (> 0.30). The estimation successfully converged
## (Rhat = 1.000) and the indices are reliable (ESS = 2277)
##   - The interaction effect of scalelatscaleEQFALSE on b assessment methodfunnel
## (Median = 2.43e-03, 95% CI [-0.03, 0.04]) has a 55.33% probability of being
## positive (> 0), 0.38% of being significant (> 0.05), and 0.00% of being large
## (> 0.30). The estimation successfully converged (Rhat = 1.000) and the indices
## are reliable (ESS = 2132)
##   - The interaction effect of scalelatscaleEQFALSE on b assessment
## methodincidentals (Median = 0.04, 95% CI [3.81e-04, 0.09]) has a 97.58%
## probability of being positive (> 0), 40.12% of being significant (> 0.05), and
## 0.00% of being large (> 0.30). The estimation successfully converged (Rhat =
## 1.000) and the indices are reliable (ESS = 2171)
##   - The interaction effect of scalelatscaleEQFALSE on b assessment
## methodspotlighting (Median = 0.04, 95% CI [-3.29e-03, 0.09]) has a 96.46%
## probability of being positive (> 0), 39.71% of being significant (> 0.05), and
## 0.00% of being large (> 0.30). The estimation successfully converged (Rhat =
## 0.999) and the indices are reliable (ESS = 2334)
##   - The interaction effect of scalelatscaleEQFALSE on b assessment
## methodcoverboard (Median = 0.05, 95% CI [-0.01, 0.11]) has a 94.21% probability
## of being positive (> 0), 45.88% of being significant (> 0.05), and 0.00% of
## being large (> 0.30). The estimation successfully converged (Rhat = 1.002) and
## the indices are reliable (ESS = 1302)
##   - The interaction effect of scalelatscaleEQFALSE on b assessment methodcamera
## (Median = -0.03, 95% CI [-0.11, 0.05]) has a 75.71% probability of being
## negative (< 0), 30.63% of being significant (< -0.05), and 0.00% of being large
## (< -0.30). The estimation successfully converged (Rhat = 1.001) and the indices
## are reliable (ESS = 1663)
##   - NANAThe estimation successfully converged (Rhat = 1.000) and the indices are
## reliable (ESS = 2331)
##   - NANAThe estimation successfully converged (Rhat = 1.002) and the indices are
## reliable (ESS = 2179)
##   - NANAThe estimation successfully converged (Rhat = 0.999) and the indices are
## reliable (ESS = 2347)
##   - NANAThe estimation successfully converged (Rhat = 1.000) and the indices are
## reliable (ESS = 2200)
## 
## Following the Sequential Effect eXistence and sIgnificance Testing (SEXIT)
## framework, we report the median of the posterior distribution and its 95% CI
## (Highest Density Interval), along the probability of direction (pd), the
## probability of significance and the probability of being large. The thresholds
## beyond which the effect is considered as significant (i.e., non-negligible) and
## large are |0.05| and |0.30|. Convergence and stability of the Bayesian sampling
## has been assessed using R-hat, which should be below 1.01 (Vehtari et al.,
## 2019), and Effective Sample Size (ESS), which should be greater than 1000
## (Burkner, 2017)., We fitted a Bayesian poisson mixed model (estimated using
## MCMC sampling with 3 chains of 5000 iterations and a warmup of 1000) to predict
## richness with lat (formula: richness ~ assessment.method * scale(lat, scale =
## FALSE)). The model included site.plot as random effects (formula: list(~1 |
## site.plot:site, ~1 | site)). Priors over parameters were set as normal (mean =
## 0.00, SD = 3.70) distributions. The model's explanatory power is substantial
## (R2 = 0.82, 95% CI [0.77, 0.85]) and the part related to the fixed effects
## alone (marginal R2) is of 0.80 (95% CI [0.61, 0.84]).  Within this model:
## 
##   - The effect of b Intercept (Median = 1.91, 95% CI [1.55, 2.24]) has a 100.00%
## probability of being positive (> 0), 100.00% of being significant (> 0.05), and
## 100.00% of being large (> 0.30). The estimation successfully converged (Rhat =
## 1.000) and the indices are reliable (ESS = 2331)
##   - The effect of b assessment methodfunnel (Median = -0.02, 95% CI [-0.25,
## 0.21]) has a 58.83% probability of being negative (< 0), 40.54% of being
## significant (< -0.05), and 0.92% of being large (< -0.30). The estimation
## successfully converged (Rhat = 1.002) and the indices are reliable (ESS = 2179)
##   - The effect of b assessment methodincidentals (Median = -0.91, 95% CI [-1.24,
## -0.61]) has a 100.00% probability of being negative (< 0), 100.00% of being
## significant (< -0.05), and 100.00% of being large (< -0.30). The estimation
## successfully converged (Rhat = 0.999) and the indices are reliable (ESS = 2347)
##   - The effect of b assessment methodspotlighting (Median = -1.11, 95% CI [-1.45,
## -0.78]) has a 100.00% probability of being negative (< 0), 100.00% of being
## significant (< -0.05), and 100.00% of being large (< -0.30). The estimation
## successfully converged (Rhat = 1.000) and the indices are reliable (ESS = 2200)
##   - The effect of b assessment methodcoverboard (Median = -1.57, 95% CI [-2.01,
## -1.17]) has a 100.00% probability of being negative (< 0), 100.00% of being
## significant (< -0.05), and 100.00% of being large (< -0.30). The estimation
## successfully converged (Rhat = 1.000) and the indices are reliable (ESS = 2048)
##   - The effect of b assessment methodcamera (Median = -2.48, 95% CI [-3.09,
## -1.94]) has a 100.00% probability of being negative (< 0), 100.00% of being
## significant (< -0.05), and 100.00% of being large (< -0.30). The estimation
## successfully converged (Rhat = 1.003) and the indices are reliable (ESS = 1697)
##   - The effect of b scalelatscaleEQFALSE (Median = 0.07, 95% CI [0.02, 0.12]) has
## a 99.54% probability of being positive (> 0), 84.58% of being significant (>
## 0.05), and 0.00% of being large (> 0.30). The estimation successfully converged
## (Rhat = 1.000) and the indices are reliable (ESS = 2277)
##   - The interaction effect of scalelatscaleEQFALSE on b assessment methodfunnel
## (Median = 2.43e-03, 95% CI [-0.03, 0.04]) has a 55.33% probability of being
## positive (> 0), 0.38% of being significant (> 0.05), and 0.00% of being large
## (> 0.30). The estimation successfully converged (Rhat = 1.000) and the indices
## are reliable (ESS = 2132)
##   - The interaction effect of scalelatscaleEQFALSE on b assessment
## methodincidentals (Median = 0.04, 95% CI [3.81e-04, 0.09]) has a 97.58%
## probability of being positive (> 0), 40.12% of being significant (> 0.05), and
## 0.00% of being large (> 0.30). The estimation successfully converged (Rhat =
## 1.000) and the indices are reliable (ESS = 2171)
##   - The interaction effect of scalelatscaleEQFALSE on b assessment
## methodspotlighting (Median = 0.04, 95% CI [-3.29e-03, 0.09]) has a 96.46%
## probability of being positive (> 0), 39.71% of being significant (> 0.05), and
## 0.00% of being large (> 0.30). The estimation successfully converged (Rhat =
## 0.999) and the indices are reliable (ESS = 2334)
##   - The interaction effect of scalelatscaleEQFALSE on b assessment
## methodcoverboard (Median = 0.05, 95% CI [-0.01, 0.11]) has a 94.21% probability
## of being positive (> 0), 45.88% of being significant (> 0.05), and 0.00% of
## being large (> 0.30). The estimation successfully converged (Rhat = 1.002) and
## the indices are reliable (ESS = 1302)
##   - The interaction effect of scalelatscaleEQFALSE on b assessment methodcamera
## (Median = -0.03, 95% CI [-0.11, 0.05]) has a 75.71% probability of being
## negative (< 0), 30.63% of being significant (< -0.05), and 0.00% of being large
## (< -0.30). The estimation successfully converged (Rhat = 1.001) and the indices
## are reliable (ESS = 1663)
##   - NANAThe estimation successfully converged (Rhat = 1.000) and the indices are
## reliable (ESS = 2331)
##   - NANAThe estimation successfully converged (Rhat = 1.002) and the indices are
## reliable (ESS = 2179)
##   - NANAThe estimation successfully converged (Rhat = 0.999) and the indices are
## reliable (ESS = 2347)
##   - NANAThe estimation successfully converged (Rhat = 1.000) and the indices are
## reliable (ESS = 2200)
## 
## Following the Sequential Effect eXistence and sIgnificance Testing (SEXIT)
## framework, we report the median of the posterior distribution and its 95% CI
## (Highest Density Interval), along the probability of direction (pd), the
## probability of significance and the probability of being large. The thresholds
## beyond which the effect is considered as significant (i.e., non-negligible) and
## large are |0.05| and |0.30|. Convergence and stability of the Bayesian sampling
## has been assessed using R-hat, which should be below 1.01 (Vehtari et al.,
## 2019), and Effective Sample Size (ESS), which should be greater than 1000
## (Burkner, 2017)., We fitted a Bayesian poisson mixed model (estimated using
## MCMC sampling with 3 chains of 5000 iterations and a warmup of 1000) to predict
## richness with assessment.method (formula: richness ~ assessment.method *
## scale(lat, scale = FALSE)). The model included site.plot as random effects
## (formula: list(~1 | site.plot:site, ~1 | site)). Priors over parameters were
## set as normal (mean = 0.00, SD = 3.70) distributions. The model's explanatory
## power is substantial (R2 = 0.82, 95% CI [0.77, 0.85]) and the part related to
## the fixed effects alone (marginal R2) is of 0.80 (95% CI [0.61, 0.84]).  Within
## this model:
## 
##   - The effect of b Intercept (Median = 1.91, 95% CI [1.55, 2.24]) has a 100.00%
## probability of being positive (> 0), 100.00% of being significant (> 0.05), and
## 100.00% of being large (> 0.30). The estimation successfully converged (Rhat =
## 1.000) and the indices are reliable (ESS = 2331)
##   - The effect of b assessment methodfunnel (Median = -0.02, 95% CI [-0.25,
## 0.21]) has a 58.83% probability of being negative (< 0), 40.54% of being
## significant (< -0.05), and 0.92% of being large (< -0.30). The estimation
## successfully converged (Rhat = 1.002) and the indices are reliable (ESS = 2179)
##   - The effect of b assessment methodincidentals (Median = -0.91, 95% CI [-1.24,
## -0.61]) has a 100.00% probability of being negative (< 0), 100.00% of being
## significant (< -0.05), and 100.00% of being large (< -0.30). The estimation
## successfully converged (Rhat = 0.999) and the indices are reliable (ESS = 2347)
##   - The effect of b assessment methodspotlighting (Median = -1.11, 95% CI [-1.45,
## -0.78]) has a 100.00% probability of being negative (< 0), 100.00% of being
## significant (< -0.05), and 100.00% of being large (< -0.30). The estimation
## successfully converged (Rhat = 1.000) and the indices are reliable (ESS = 2200)
##   - The effect of b assessment methodcoverboard (Median = -1.57, 95% CI [-2.01,
## -1.17]) has a 100.00% probability of being negative (< 0), 100.00% of being
## significant (< -0.05), and 100.00% of being large (< -0.30). The estimation
## successfully converged (Rhat = 1.000) and the indices are reliable (ESS = 2048)
##   - The effect of b assessment methodcamera (Median = -2.48, 95% CI [-3.09,
## -1.94]) has a 100.00% probability of being negative (< 0), 100.00% of being
## significant (< -0.05), and 100.00% of being large (< -0.30). The estimation
## successfully converged (Rhat = 1.003) and the indices are reliable (ESS = 1697)
##   - The effect of b scalelatscaleEQFALSE (Median = 0.07, 95% CI [0.02, 0.12]) has
## a 99.54% probability of being positive (> 0), 84.58% of being significant (>
## 0.05), and 0.00% of being large (> 0.30). The estimation successfully converged
## (Rhat = 1.000) and the indices are reliable (ESS = 2277)
##   - The interaction effect of scalelatscaleEQFALSE on b assessment methodfunnel
## (Median = 2.43e-03, 95% CI [-0.03, 0.04]) has a 55.33% probability of being
## positive (> 0), 0.38% of being significant (> 0.05), and 0.00% of being large
## (> 0.30). The estimation successfully converged (Rhat = 1.000) and the indices
## are reliable (ESS = 2132)
##   - The interaction effect of scalelatscaleEQFALSE on b assessment
## methodincidentals (Median = 0.04, 95% CI [3.81e-04, 0.09]) has a 97.58%
## probability of being positive (> 0), 40.12% of being significant (> 0.05), and
## 0.00% of being large (> 0.30). The estimation successfully converged (Rhat =
## 1.000) and the indices are reliable (ESS = 2171)
##   - The interaction effect of scalelatscaleEQFALSE on b assessment
## methodspotlighting (Median = 0.04, 95% CI [-3.29e-03, 0.09]) has a 96.46%
## probability of being positive (> 0), 39.71% of being significant (> 0.05), and
## 0.00% of being large (> 0.30). The estimation successfully converged (Rhat =
## 0.999) and the indices are reliable (ESS = 2334)
##   - The interaction effect of scalelatscaleEQFALSE on b assessment
## methodcoverboard (Median = 0.05, 95% CI [-0.01, 0.11]) has a 94.21% probability
## of being positive (> 0), 45.88% of being significant (> 0.05), and 0.00% of
## being large (> 0.30). The estimation successfully converged (Rhat = 1.002) and
## the indices are reliable (ESS = 1302)
##   - The interaction effect of scalelatscaleEQFALSE on b assessment methodcamera
## (Median = -0.03, 95% CI [-0.11, 0.05]) has a 75.71% probability of being
## negative (< 0), 30.63% of being significant (< -0.05), and 0.00% of being large
## (< -0.30). The estimation successfully converged (Rhat = 1.001) and the indices
## are reliable (ESS = 1663)
##   - NANAThe estimation successfully converged (Rhat = 1.000) and the indices are
## reliable (ESS = 2331)
##   - NANAThe estimation successfully converged (Rhat = 1.002) and the indices are
## reliable (ESS = 2179)
##   - NANAThe estimation successfully converged (Rhat = 0.999) and the indices are
## reliable (ESS = 2347)
##   - NANAThe estimation successfully converged (Rhat = 1.000) and the indices are
## reliable (ESS = 2200)
## 
## Following the Sequential Effect eXistence and sIgnificance Testing (SEXIT)
## framework, we report the median of the posterior distribution and its 95% CI
## (Highest Density Interval), along the probability of direction (pd), the
## probability of significance and the probability of being large. The thresholds
## beyond which the effect is considered as significant (i.e., non-negligible) and
## large are |0.05| and |0.30|. Convergence and stability of the Bayesian sampling
## has been assessed using R-hat, which should be below 1.01 (Vehtari et al.,
## 2019), and Effective Sample Size (ESS), which should be greater than 1000
## (Burkner, 2017)., We fitted a Bayesian poisson mixed model (estimated using
## MCMC sampling with 3 chains of 5000 iterations and a warmup of 1000) to predict
## richness with lat (formula: richness ~ assessment.method * scale(lat, scale =
## FALSE)). The model included site.plot as random effects (formula: list(~1 |
## site.plot:site, ~1 | site)). Priors over parameters were set as normal (mean =
## 0.00, SD = 3.70) distributions. The model's explanatory power is substantial
## (R2 = 0.82, 95% CI [0.77, 0.85]) and the part related to the fixed effects
## alone (marginal R2) is of 0.80 (95% CI [0.61, 0.84]).  Within this model:
## 
##   - The effect of b Intercept (Median = 1.91, 95% CI [1.55, 2.24]) has a 100.00%
## probability of being positive (> 0), 100.00% of being significant (> 0.05), and
## 100.00% of being large (> 0.30). The estimation successfully converged (Rhat =
## 1.000) and the indices are reliable (ESS = 2331)
##   - The effect of b assessment methodfunnel (Median = -0.02, 95% CI [-0.25,
## 0.21]) has a 58.83% probability of being negative (< 0), 40.54% of being
## significant (< -0.05), and 0.92% of being large (< -0.30). The estimation
## successfully converged (Rhat = 1.002) and the indices are reliable (ESS = 2179)
##   - The effect of b assessment methodincidentals (Median = -0.91, 95% CI [-1.24,
## -0.61]) has a 100.00% probability of being negative (< 0), 100.00% of being
## significant (< -0.05), and 100.00% of being large (< -0.30). The estimation
## successfully converged (Rhat = 0.999) and the indices are reliable (ESS = 2347)
##   - The effect of b assessment methodspotlighting (Median = -1.11, 95% CI [-1.45,
## -0.78]) has a 100.00% probability of being negative (< 0), 100.00% of being
## significant (< -0.05), and 100.00% of being large (< -0.30). The estimation
## successfully converged (Rhat = 1.000) and the indices are reliable (ESS = 2200)
##   - The effect of b assessment methodcoverboard (Median = -1.57, 95% CI [-2.01,
## -1.17]) has a 100.00% probability of being negative (< 0), 100.00% of being
## significant (< -0.05), and 100.00% of being large (< -0.30). The estimation
## successfully converged (Rhat = 1.000) and the indices are reliable (ESS = 2048)
##   - The effect of b assessment methodcamera (Median = -2.48, 95% CI [-3.09,
## -1.94]) has a 100.00% probability of being negative (< 0), 100.00% of being
## significant (< -0.05), and 100.00% of being large (< -0.30). The estimation
## successfully converged (Rhat = 1.003) and the indices are reliable (ESS = 1697)
##   - The effect of b scalelatscaleEQFALSE (Median = 0.07, 95% CI [0.02, 0.12]) has
## a 99.54% probability of being positive (> 0), 84.58% of being significant (>
## 0.05), and 0.00% of being large (> 0.30). The estimation successfully converged
## (Rhat = 1.000) and the indices are reliable (ESS = 2277)
##   - The interaction effect of scalelatscaleEQFALSE on b assessment methodfunnel
## (Median = 2.43e-03, 95% CI [-0.03, 0.04]) has a 55.33% probability of being
## positive (> 0), 0.38% of being significant (> 0.05), and 0.00% of being large
## (> 0.30). The estimation successfully converged (Rhat = 1.000) and the indices
## are reliable (ESS = 2132)
##   - The interaction effect of scalelatscaleEQFALSE on b assessment
## methodincidentals (Median = 0.04, 95% CI [3.81e-04, 0.09]) has a 97.58%
## probability of being positive (> 0), 40.12% of being significant (> 0.05), and
## 0.00% of being large (> 0.30). The estimation successfully converged (Rhat =
## 1.000) and the indices are reliable (ESS = 2171)
##   - The interaction effect of scalelatscaleEQFALSE on b assessment
## methodspotlighting (Median = 0.04, 95% CI [-3.29e-03, 0.09]) has a 96.46%
## probability of being positive (> 0), 39.71% of being significant (> 0.05), and
## 0.00% of being large (> 0.30). The estimation successfully converged (Rhat =
## 0.999) and the indices are reliable (ESS = 2334)
##   - The interaction effect of scalelatscaleEQFALSE on b assessment
## methodcoverboard (Median = 0.05, 95% CI [-0.01, 0.11]) has a 94.21% probability
## of being positive (> 0), 45.88% of being significant (> 0.05), and 0.00% of
## being large (> 0.30). The estimation successfully converged (Rhat = 1.002) and
## the indices are reliable (ESS = 1302)
##   - The interaction effect of scalelatscaleEQFALSE on b assessment methodcamera
## (Median = -0.03, 95% CI [-0.11, 0.05]) has a 75.71% probability of being
## negative (< 0), 30.63% of being significant (< -0.05), and 0.00% of being large
## (< -0.30). The estimation successfully converged (Rhat = 1.001) and the indices
## are reliable (ESS = 1663)
##   - NANAThe estimation successfully converged (Rhat = 1.000) and the indices are
## reliable (ESS = 2331)
##   - NANAThe estimation successfully converged (Rhat = 1.002) and the indices are
## reliable (ESS = 2179)
##   - NANAThe estimation successfully converged (Rhat = 0.999) and the indices are
## reliable (ESS = 2347)
##   - NANAThe estimation successfully converged (Rhat = 1.000) and the indices are
## reliable (ESS = 2200)
## 
## Following the Sequential Effect eXistence and sIgnificance Testing (SEXIT)
## framework, we report the median of the posterior distribution and its 95% CI
## (Highest Density Interval), along the probability of direction (pd), the
## probability of significance and the probability of being large. The thresholds
## beyond which the effect is considered as significant (i.e., non-negligible) and
## large are |0.05| and |0.30|. Convergence and stability of the Bayesian sampling
## has been assessed using R-hat, which should be below 1.01 (Vehtari et al.,
## 2019), and Effective Sample Size (ESS), which should be greater than 1000
## (Burkner, 2017)., We fitted a Bayesian poisson mixed model (estimated using
## MCMC sampling with 3 chains of 5000 iterations and a warmup of 1000) to predict
## richness with assessment.method (formula: richness ~ assessment.method *
## scale(lat, scale = FALSE)). The model included site.plot as random effects
## (formula: list(~1 | site.plot:site, ~1 | site)). Priors over parameters were
## set as student_t (location = 0.00, scale = 3.70) distributions. The model's
## explanatory power is substantial (R2 = 0.82, 95% CI [0.77, 0.85]) and the part
## related to the fixed effects alone (marginal R2) is of 0.80 (95% CI [0.61,
## 0.84]).  Within this model:
## 
##   - The effect of b Intercept (Median = 1.91, 95% CI [1.55, 2.24]) has a 100.00%
## probability of being positive (> 0), 100.00% of being significant (> 0.05), and
## 100.00% of being large (> 0.30). The estimation successfully converged (Rhat =
## 1.000) and the indices are reliable (ESS = 2331)
##   - The effect of b assessment methodfunnel (Median = -0.02, 95% CI [-0.25,
## 0.21]) has a 58.83% probability of being negative (< 0), 40.54% of being
## significant (< -0.05), and 0.92% of being large (< -0.30). The estimation
## successfully converged (Rhat = 1.002) and the indices are reliable (ESS = 2179)
##   - The effect of b assessment methodincidentals (Median = -0.91, 95% CI [-1.24,
## -0.61]) has a 100.00% probability of being negative (< 0), 100.00% of being
## significant (< -0.05), and 100.00% of being large (< -0.30). The estimation
## successfully converged (Rhat = 0.999) and the indices are reliable (ESS = 2347)
##   - The effect of b assessment methodspotlighting (Median = -1.11, 95% CI [-1.45,
## -0.78]) has a 100.00% probability of being negative (< 0), 100.00% of being
## significant (< -0.05), and 100.00% of being large (< -0.30). The estimation
## successfully converged (Rhat = 1.000) and the indices are reliable (ESS = 2200)
##   - The effect of b assessment methodcoverboard (Median = -1.57, 95% CI [-2.01,
## -1.17]) has a 100.00% probability of being negative (< 0), 100.00% of being
## significant (< -0.05), and 100.00% of being large (< -0.30). The estimation
## successfully converged (Rhat = 1.000) and the indices are reliable (ESS = 2048)
##   - The effect of b assessment methodcamera (Median = -2.48, 95% CI [-3.09,
## -1.94]) has a 100.00% probability of being negative (< 0), 100.00% of being
## significant (< -0.05), and 100.00% of being large (< -0.30). The estimation
## successfully converged (Rhat = 1.003) and the indices are reliable (ESS = 1697)
##   - The effect of b scalelatscaleEQFALSE (Median = 0.07, 95% CI [0.02, 0.12]) has
## a 99.54% probability of being positive (> 0), 84.58% of being significant (>
## 0.05), and 0.00% of being large (> 0.30). The estimation successfully converged
## (Rhat = 1.000) and the indices are reliable (ESS = 2277)
##   - The interaction effect of scalelatscaleEQFALSE on b assessment methodfunnel
## (Median = 2.43e-03, 95% CI [-0.03, 0.04]) has a 55.33% probability of being
## positive (> 0), 0.38% of being significant (> 0.05), and 0.00% of being large
## (> 0.30). The estimation successfully converged (Rhat = 1.000) and the indices
## are reliable (ESS = 2132)
##   - The interaction effect of scalelatscaleEQFALSE on b assessment
## methodincidentals (Median = 0.04, 95% CI [3.81e-04, 0.09]) has a 97.58%
## probability of being positive (> 0), 40.12% of being significant (> 0.05), and
## 0.00% of being large (> 0.30). The estimation successfully converged (Rhat =
## 1.000) and the indices are reliable (ESS = 2171)
##   - The interaction effect of scalelatscaleEQFALSE on b assessment
## methodspotlighting (Median = 0.04, 95% CI [-3.29e-03, 0.09]) has a 96.46%
## probability of being positive (> 0), 39.71% of being significant (> 0.05), and
## 0.00% of being large (> 0.30). The estimation successfully converged (Rhat =
## 0.999) and the indices are reliable (ESS = 2334)
##   - The interaction effect of scalelatscaleEQFALSE on b assessment
## methodcoverboard (Median = 0.05, 95% CI [-0.01, 0.11]) has a 94.21% probability
## of being positive (> 0), 45.88% of being significant (> 0.05), and 0.00% of
## being large (> 0.30). The estimation successfully converged (Rhat = 1.002) and
## the indices are reliable (ESS = 1302)
##   - The interaction effect of scalelatscaleEQFALSE on b assessment methodcamera
## (Median = -0.03, 95% CI [-0.11, 0.05]) has a 75.71% probability of being
## negative (< 0), 30.63% of being significant (< -0.05), and 0.00% of being large
## (< -0.30). The estimation successfully converged (Rhat = 1.001) and the indices
## are reliable (ESS = 1663)
##   - NANAThe estimation successfully converged (Rhat = 1.000) and the indices are
## reliable (ESS = 2331)
##   - NANAThe estimation successfully converged (Rhat = 1.002) and the indices are
## reliable (ESS = 2179)
##   - NANAThe estimation successfully converged (Rhat = 0.999) and the indices are
## reliable (ESS = 2347)
##   - NANAThe estimation successfully converged (Rhat = 1.000) and the indices are
## reliable (ESS = 2200)
## 
## Following the Sequential Effect eXistence and sIgnificance Testing (SEXIT)
## framework, we report the median of the posterior distribution and its 95% CI
## (Highest Density Interval), along the probability of direction (pd), the
## probability of significance and the probability of being large. The thresholds
## beyond which the effect is considered as significant (i.e., non-negligible) and
## large are |0.05| and |0.30|. Convergence and stability of the Bayesian sampling
## has been assessed using R-hat, which should be below 1.01 (Vehtari et al.,
## 2019), and Effective Sample Size (ESS), which should be greater than 1000
## (Burkner, 2017)., We fitted a Bayesian poisson mixed model (estimated using
## MCMC sampling with 3 chains of 5000 iterations and a warmup of 1000) to predict
## richness with lat (formula: richness ~ assessment.method * scale(lat, scale =
## FALSE)). The model included site.plot as random effects (formula: list(~1 |
## site.plot:site, ~1 | site)). Priors over parameters were set as student_t
## (location = 0.00, scale = 3.70) distributions. The model's explanatory power is
## substantial (R2 = 0.82, 95% CI [0.77, 0.85]) and the part related to the fixed
## effects alone (marginal R2) is of 0.80 (95% CI [0.61, 0.84]).  Within this
## model:
## 
##   - The effect of b Intercept (Median = 1.91, 95% CI [1.55, 2.24]) has a 100.00%
## probability of being positive (> 0), 100.00% of being significant (> 0.05), and
## 100.00% of being large (> 0.30). The estimation successfully converged (Rhat =
## 1.000) and the indices are reliable (ESS = 2331)
##   - The effect of b assessment methodfunnel (Median = -0.02, 95% CI [-0.25,
## 0.21]) has a 58.83% probability of being negative (< 0), 40.54% of being
## significant (< -0.05), and 0.92% of being large (< -0.30). The estimation
## successfully converged (Rhat = 1.002) and the indices are reliable (ESS = 2179)
##   - The effect of b assessment methodincidentals (Median = -0.91, 95% CI [-1.24,
## -0.61]) has a 100.00% probability of being negative (< 0), 100.00% of being
## significant (< -0.05), and 100.00% of being large (< -0.30). The estimation
## successfully converged (Rhat = 0.999) and the indices are reliable (ESS = 2347)
##   - The effect of b assessment methodspotlighting (Median = -1.11, 95% CI [-1.45,
## -0.78]) has a 100.00% probability of being negative (< 0), 100.00% of being
## significant (< -0.05), and 100.00% of being large (< -0.30). The estimation
## successfully converged (Rhat = 1.000) and the indices are reliable (ESS = 2200)
##   - The effect of b assessment methodcoverboard (Median = -1.57, 95% CI [-2.01,
## -1.17]) has a 100.00% probability of being negative (< 0), 100.00% of being
## significant (< -0.05), and 100.00% of being large (< -0.30). The estimation
## successfully converged (Rhat = 1.000) and the indices are reliable (ESS = 2048)
##   - The effect of b assessment methodcamera (Median = -2.48, 95% CI [-3.09,
## -1.94]) has a 100.00% probability of being negative (< 0), 100.00% of being
## significant (< -0.05), and 100.00% of being large (< -0.30). The estimation
## successfully converged (Rhat = 1.003) and the indices are reliable (ESS = 1697)
##   - The effect of b scalelatscaleEQFALSE (Median = 0.07, 95% CI [0.02, 0.12]) has
## a 99.54% probability of being positive (> 0), 84.58% of being significant (>
## 0.05), and 0.00% of being large (> 0.30). The estimation successfully converged
## (Rhat = 1.000) and the indices are reliable (ESS = 2277)
##   - The interaction effect of scalelatscaleEQFALSE on b assessment methodfunnel
## (Median = 2.43e-03, 95% CI [-0.03, 0.04]) has a 55.33% probability of being
## positive (> 0), 0.38% of being significant (> 0.05), and 0.00% of being large
## (> 0.30). The estimation successfully converged (Rhat = 1.000) and the indices
## are reliable (ESS = 2132)
##   - The interaction effect of scalelatscaleEQFALSE on b assessment
## methodincidentals (Median = 0.04, 95% CI [3.81e-04, 0.09]) has a 97.58%
## probability of being positive (> 0), 40.12% of being significant (> 0.05), and
## 0.00% of being large (> 0.30). The estimation successfully converged (Rhat =
## 1.000) and the indices are reliable (ESS = 2171)
##   - The interaction effect of scalelatscaleEQFALSE on b assessment
## methodspotlighting (Median = 0.04, 95% CI [-3.29e-03, 0.09]) has a 96.46%
## probability of being positive (> 0), 39.71% of being significant (> 0.05), and
## 0.00% of being large (> 0.30). The estimation successfully converged (Rhat =
## 0.999) and the indices are reliable (ESS = 2334)
##   - The interaction effect of scalelatscaleEQFALSE on b assessment
## methodcoverboard (Median = 0.05, 95% CI [-0.01, 0.11]) has a 94.21% probability
## of being positive (> 0), 45.88% of being significant (> 0.05), and 0.00% of
## being large (> 0.30). The estimation successfully converged (Rhat = 1.002) and
## the indices are reliable (ESS = 1302)
##   - The interaction effect of scalelatscaleEQFALSE on b assessment methodcamera
## (Median = -0.03, 95% CI [-0.11, 0.05]) has a 75.71% probability of being
## negative (< 0), 30.63% of being significant (< -0.05), and 0.00% of being large
## (< -0.30). The estimation successfully converged (Rhat = 1.001) and the indices
## are reliable (ESS = 1663)
##   - NANAThe estimation successfully converged (Rhat = 1.000) and the indices are
## reliable (ESS = 2331)
##   - NANAThe estimation successfully converged (Rhat = 1.002) and the indices are
## reliable (ESS = 2179)
##   - NANAThe estimation successfully converged (Rhat = 0.999) and the indices are
## reliable (ESS = 2347)
##   - NANAThe estimation successfully converged (Rhat = 1.000) and the indices are
## reliable (ESS = 2200)
## 
## Following the Sequential Effect eXistence and sIgnificance Testing (SEXIT)
## framework, we report the median of the posterior distribution and its 95% CI
## (Highest Density Interval), along the probability of direction (pd), the
## probability of significance and the probability of being large. The thresholds
## beyond which the effect is considered as significant (i.e., non-negligible) and
## large are |0.05| and |0.30|. Convergence and stability of the Bayesian sampling
## has been assessed using R-hat, which should be below 1.01 (Vehtari et al.,
## 2019), and Effective Sample Size (ESS), which should be greater than 1000
## (Burkner, 2017)., We fitted a Bayesian poisson mixed model (estimated using
## MCMC sampling with 3 chains of 5000 iterations and a warmup of 1000) to predict
## richness with assessment.method (formula: richness ~ assessment.method *
## scale(lat, scale = FALSE)). The model included site.plot as random effects
## (formula: list(~1 | site.plot:site, ~1 | site)). Priors over parameters were
## set as NA (NA) distributions. The model's explanatory power is substantial (R2
## = 0.82, 95% CI [0.77, 0.85]) and the part related to the fixed effects alone
## (marginal R2) is of 0.80 (95% CI [0.61, 0.84]).  Within this model:
## 
##   - The effect of b Intercept (Median = 1.91, 95% CI [1.55, 2.24]) has a 100.00%
## probability of being positive (> 0), 100.00% of being significant (> 0.05), and
## 100.00% of being large (> 0.30). The estimation successfully converged (Rhat =
## 1.000) and the indices are reliable (ESS = 2331)
##   - The effect of b assessment methodfunnel (Median = -0.02, 95% CI [-0.25,
## 0.21]) has a 58.83% probability of being negative (< 0), 40.54% of being
## significant (< -0.05), and 0.92% of being large (< -0.30). The estimation
## successfully converged (Rhat = 1.002) and the indices are reliable (ESS = 2179)
##   - The effect of b assessment methodincidentals (Median = -0.91, 95% CI [-1.24,
## -0.61]) has a 100.00% probability of being negative (< 0), 100.00% of being
## significant (< -0.05), and 100.00% of being large (< -0.30). The estimation
## successfully converged (Rhat = 0.999) and the indices are reliable (ESS = 2347)
##   - The effect of b assessment methodspotlighting (Median = -1.11, 95% CI [-1.45,
## -0.78]) has a 100.00% probability of being negative (< 0), 100.00% of being
## significant (< -0.05), and 100.00% of being large (< -0.30). The estimation
## successfully converged (Rhat = 1.000) and the indices are reliable (ESS = 2200)
##   - The effect of b assessment methodcoverboard (Median = -1.57, 95% CI [-2.01,
## -1.17]) has a 100.00% probability of being negative (< 0), 100.00% of being
## significant (< -0.05), and 100.00% of being large (< -0.30). The estimation
## successfully converged (Rhat = 1.000) and the indices are reliable (ESS = 2048)
##   - The effect of b assessment methodcamera (Median = -2.48, 95% CI [-3.09,
## -1.94]) has a 100.00% probability of being negative (< 0), 100.00% of being
## significant (< -0.05), and 100.00% of being large (< -0.30). The estimation
## successfully converged (Rhat = 1.003) and the indices are reliable (ESS = 1697)
##   - The effect of b scalelatscaleEQFALSE (Median = 0.07, 95% CI [0.02, 0.12]) has
## a 99.54% probability of being positive (> 0), 84.58% of being significant (>
## 0.05), and 0.00% of being large (> 0.30). The estimation successfully converged
## (Rhat = 1.000) and the indices are reliable (ESS = 2277)
##   - The interaction effect of scalelatscaleEQFALSE on b assessment methodfunnel
## (Median = 2.43e-03, 95% CI [-0.03, 0.04]) has a 55.33% probability of being
## positive (> 0), 0.38% of being significant (> 0.05), and 0.00% of being large
## (> 0.30). The estimation successfully converged (Rhat = 1.000) and the indices
## are reliable (ESS = 2132)
##   - The interaction effect of scalelatscaleEQFALSE on b assessment
## methodincidentals (Median = 0.04, 95% CI [3.81e-04, 0.09]) has a 97.58%
## probability of being positive (> 0), 40.12% of being significant (> 0.05), and
## 0.00% of being large (> 0.30). The estimation successfully converged (Rhat =
## 1.000) and the indices are reliable (ESS = 2171)
##   - The interaction effect of scalelatscaleEQFALSE on b assessment
## methodspotlighting (Median = 0.04, 95% CI [-3.29e-03, 0.09]) has a 96.46%
## probability of being positive (> 0), 39.71% of being significant (> 0.05), and
## 0.00% of being large (> 0.30). The estimation successfully converged (Rhat =
## 0.999) and the indices are reliable (ESS = 2334)
##   - The interaction effect of scalelatscaleEQFALSE on b assessment
## methodcoverboard (Median = 0.05, 95% CI [-0.01, 0.11]) has a 94.21% probability
## of being positive (> 0), 45.88% of being significant (> 0.05), and 0.00% of
## being large (> 0.30). The estimation successfully converged (Rhat = 1.002) and
## the indices are reliable (ESS = 1302)
##   - The interaction effect of scalelatscaleEQFALSE on b assessment methodcamera
## (Median = -0.03, 95% CI [-0.11, 0.05]) has a 75.71% probability of being
## negative (< 0), 30.63% of being significant (< -0.05), and 0.00% of being large
## (< -0.30). The estimation successfully converged (Rhat = 1.001) and the indices
## are reliable (ESS = 1663)
##   - NANAThe estimation successfully converged (Rhat = 1.000) and the indices are
## reliable (ESS = 2331)
##   - NANAThe estimation successfully converged (Rhat = 1.002) and the indices are
## reliable (ESS = 2179)
##   - NANAThe estimation successfully converged (Rhat = 0.999) and the indices are
## reliable (ESS = 2347)
##   - NANAThe estimation successfully converged (Rhat = 1.000) and the indices are
## reliable (ESS = 2200)
## 
## Following the Sequential Effect eXistence and sIgnificance Testing (SEXIT)
## framework, we report the median of the posterior distribution and its 95% CI
## (Highest Density Interval), along the probability of direction (pd), the
## probability of significance and the probability of being large. The thresholds
## beyond which the effect is considered as significant (i.e., non-negligible) and
## large are |0.05| and |0.30|. Convergence and stability of the Bayesian sampling
## has been assessed using R-hat, which should be below 1.01 (Vehtari et al.,
## 2019), and Effective Sample Size (ESS), which should be greater than 1000
## (Burkner, 2017)., We fitted a Bayesian poisson mixed model (estimated using
## MCMC sampling with 3 chains of 5000 iterations and a warmup of 1000) to predict
## richness with lat (formula: richness ~ assessment.method * scale(lat, scale =
## FALSE)). The model included site.plot as random effects (formula: list(~1 |
## site.plot:site, ~1 | site)). Priors over parameters were set as NA (NA)
## distributions. The model's explanatory power is substantial (R2 = 0.82, 95% CI
## [0.77, 0.85]) and the part related to the fixed effects alone (marginal R2) is
## of 0.80 (95% CI [0.61, 0.84]).  Within this model:
## 
##   - The effect of b Intercept (Median = 1.91, 95% CI [1.55, 2.24]) has a 100.00%
## probability of being positive (> 0), 100.00% of being significant (> 0.05), and
## 100.00% of being large (> 0.30). The estimation successfully converged (Rhat =
## 1.000) and the indices are reliable (ESS = 2331)
##   - The effect of b assessment methodfunnel (Median = -0.02, 95% CI [-0.25,
## 0.21]) has a 58.83% probability of being negative (< 0), 40.54% of being
## significant (< -0.05), and 0.92% of being large (< -0.30). The estimation
## successfully converged (Rhat = 1.002) and the indices are reliable (ESS = 2179)
##   - The effect of b assessment methodincidentals (Median = -0.91, 95% CI [-1.24,
## -0.61]) has a 100.00% probability of being negative (< 0), 100.00% of being
## significant (< -0.05), and 100.00% of being large (< -0.30). The estimation
## successfully converged (Rhat = 0.999) and the indices are reliable (ESS = 2347)
##   - The effect of b assessment methodspotlighting (Median = -1.11, 95% CI [-1.45,
## -0.78]) has a 100.00% probability of being negative (< 0), 100.00% of being
## significant (< -0.05), and 100.00% of being large (< -0.30). The estimation
## successfully converged (Rhat = 1.000) and the indices are reliable (ESS = 2200)
##   - The effect of b assessment methodcoverboard (Median = -1.57, 95% CI [-2.01,
## -1.17]) has a 100.00% probability of being negative (< 0), 100.00% of being
## significant (< -0.05), and 100.00% of being large (< -0.30). The estimation
## successfully converged (Rhat = 1.000) and the indices are reliable (ESS = 2048)
##   - The effect of b assessment methodcamera (Median = -2.48, 95% CI [-3.09,
## -1.94]) has a 100.00% probability of being negative (< 0), 100.00% of being
## significant (< -0.05), and 100.00% of being large (< -0.30). The estimation
## successfully converged (Rhat = 1.003) and the indices are reliable (ESS = 1697)
##   - The effect of b scalelatscaleEQFALSE (Median = 0.07, 95% CI [0.02, 0.12]) has
## a 99.54% probability of being positive (> 0), 84.58% of being significant (>
## 0.05), and 0.00% of being large (> 0.30). The estimation successfully converged
## (Rhat = 1.000) and the indices are reliable (ESS = 2277)
##   - The interaction effect of scalelatscaleEQFALSE on b assessment methodfunnel
## (Median = 2.43e-03, 95% CI [-0.03, 0.04]) has a 55.33% probability of being
## positive (> 0), 0.38% of being significant (> 0.05), and 0.00% of being large
## (> 0.30). The estimation successfully converged (Rhat = 1.000) and the indices
## are reliable (ESS = 2132)
##   - The interaction effect of scalelatscaleEQFALSE on b assessment
## methodincidentals (Median = 0.04, 95% CI [3.81e-04, 0.09]) has a 97.58%
## probability of being positive (> 0), 40.12% of being significant (> 0.05), and
## 0.00% of being large (> 0.30). The estimation successfully converged (Rhat =
## 1.000) and the indices are reliable (ESS = 2171)
##   - The interaction effect of scalelatscaleEQFALSE on b assessment
## methodspotlighting (Median = 0.04, 95% CI [-3.29e-03, 0.09]) has a 96.46%
## probability of being positive (> 0), 39.71% of being significant (> 0.05), and
## 0.00% of being large (> 0.30). The estimation successfully converged (Rhat =
## 0.999) and the indices are reliable (ESS = 2334)
##   - The interaction effect of scalelatscaleEQFALSE on b assessment
## methodcoverboard (Median = 0.05, 95% CI [-0.01, 0.11]) has a 94.21% probability
## of being positive (> 0), 45.88% of being significant (> 0.05), and 0.00% of
## being large (> 0.30). The estimation successfully converged (Rhat = 1.002) and
## the indices are reliable (ESS = 1302)
##   - The interaction effect of scalelatscaleEQFALSE on b assessment methodcamera
## (Median = -0.03, 95% CI [-0.11, 0.05]) has a 75.71% probability of being
## negative (< 0), 30.63% of being significant (< -0.05), and 0.00% of being large
## (< -0.30). The estimation successfully converged (Rhat = 1.001) and the indices
## are reliable (ESS = 1663)
##   - NANAThe estimation successfully converged (Rhat = 1.000) and the indices are
## reliable (ESS = 2331)
##   - NANAThe estimation successfully converged (Rhat = 1.002) and the indices are
## reliable (ESS = 2179)
##   - NANAThe estimation successfully converged (Rhat = 0.999) and the indices are
## reliable (ESS = 2347)
##   - NANAThe estimation successfully converged (Rhat = 1.000) and the indices are
## reliable (ESS = 2200)
## 
## Following the Sequential Effect eXistence and sIgnificance Testing (SEXIT)
## framework, we report the median of the posterior distribution and its 95% CI
## (Highest Density Interval), along the probability of direction (pd), the
## probability of significance and the probability of being large. The thresholds
## beyond which the effect is considered as significant (i.e., non-negligible) and
## large are |0.05| and |0.30|. Convergence and stability of the Bayesian sampling
## has been assessed using R-hat, which should be below 1.01 (Vehtari et al.,
## 2019), and Effective Sample Size (ESS), which should be greater than 1000
## (Burkner, 2017)., We fitted a Bayesian poisson mixed model (estimated using
## MCMC sampling with 3 chains of 5000 iterations and a warmup of 1000) to predict
## richness with assessment.method (formula: richness ~ assessment.method *
## scale(lat, scale = FALSE)). The model included site.plot as random effects
## (formula: list(~1 | site.plot:site, ~1 | site)). Priors over parameters were
## set as NA (NA) distributions. The model's explanatory power is substantial (R2
## = 0.82, 95% CI [0.77, 0.85]) and the part related to the fixed effects alone
## (marginal R2) is of 0.80 (95% CI [0.61, 0.84]).  Within this model:
## 
##   - The effect of b Intercept (Median = 1.91, 95% CI [1.55, 2.24]) has a 100.00%
## probability of being positive (> 0), 100.00% of being significant (> 0.05), and
## 100.00% of being large (> 0.30). The estimation successfully converged (Rhat =
## 1.000) and the indices are reliable (ESS = 2331)
##   - The effect of b assessment methodfunnel (Median = -0.02, 95% CI [-0.25,
## 0.21]) has a 58.83% probability of being negative (< 0), 40.54% of being
## significant (< -0.05), and 0.92% of being large (< -0.30). The estimation
## successfully converged (Rhat = 1.002) and the indices are reliable (ESS = 2179)
##   - The effect of b assessment methodincidentals (Median = -0.91, 95% CI [-1.24,
## -0.61]) has a 100.00% probability of being negative (< 0), 100.00% of being
## significant (< -0.05), and 100.00% of being large (< -0.30). The estimation
## successfully converged (Rhat = 0.999) and the indices are reliable (ESS = 2347)
##   - The effect of b assessment methodspotlighting (Median = -1.11, 95% CI [-1.45,
## -0.78]) has a 100.00% probability of being negative (< 0), 100.00% of being
## significant (< -0.05), and 100.00% of being large (< -0.30). The estimation
## successfully converged (Rhat = 1.000) and the indices are reliable (ESS = 2200)
##   - The effect of b assessment methodcoverboard (Median = -1.57, 95% CI [-2.01,
## -1.17]) has a 100.00% probability of being negative (< 0), 100.00% of being
## significant (< -0.05), and 100.00% of being large (< -0.30). The estimation
## successfully converged (Rhat = 1.000) and the indices are reliable (ESS = 2048)
##   - The effect of b assessment methodcamera (Median = -2.48, 95% CI [-3.09,
## -1.94]) has a 100.00% probability of being negative (< 0), 100.00% of being
## significant (< -0.05), and 100.00% of being large (< -0.30). The estimation
## successfully converged (Rhat = 1.003) and the indices are reliable (ESS = 1697)
##   - The effect of b scalelatscaleEQFALSE (Median = 0.07, 95% CI [0.02, 0.12]) has
## a 99.54% probability of being positive (> 0), 84.58% of being significant (>
## 0.05), and 0.00% of being large (> 0.30). The estimation successfully converged
## (Rhat = 1.000) and the indices are reliable (ESS = 2277)
##   - The interaction effect of scalelatscaleEQFALSE on b assessment methodfunnel
## (Median = 2.43e-03, 95% CI [-0.03, 0.04]) has a 55.33% probability of being
## positive (> 0), 0.38% of being significant (> 0.05), and 0.00% of being large
## (> 0.30). The estimation successfully converged (Rhat = 1.000) and the indices
## are reliable (ESS = 2132)
##   - The interaction effect of scalelatscaleEQFALSE on b assessment
## methodincidentals (Median = 0.04, 95% CI [3.81e-04, 0.09]) has a 97.58%
## probability of being positive (> 0), 40.12% of being significant (> 0.05), and
## 0.00% of being large (> 0.30). The estimation successfully converged (Rhat =
## 1.000) and the indices are reliable (ESS = 2171)
##   - The interaction effect of scalelatscaleEQFALSE on b assessment
## methodspotlighting (Median = 0.04, 95% CI [-3.29e-03, 0.09]) has a 96.46%
## probability of being positive (> 0), 39.71% of being significant (> 0.05), and
## 0.00% of being large (> 0.30). The estimation successfully converged (Rhat =
## 0.999) and the indices are reliable (ESS = 2334)
##   - The interaction effect of scalelatscaleEQFALSE on b assessment
## methodcoverboard (Median = 0.05, 95% CI [-0.01, 0.11]) has a 94.21% probability
## of being positive (> 0), 45.88% of being significant (> 0.05), and 0.00% of
## being large (> 0.30). The estimation successfully converged (Rhat = 1.002) and
## the indices are reliable (ESS = 1302)
##   - The interaction effect of scalelatscaleEQFALSE on b assessment methodcamera
## (Median = -0.03, 95% CI [-0.11, 0.05]) has a 75.71% probability of being
## negative (< 0), 30.63% of being significant (< -0.05), and 0.00% of being large
## (< -0.30). The estimation successfully converged (Rhat = 1.001) and the indices
## are reliable (ESS = 1663)
##   - NANAThe estimation successfully converged (Rhat = 1.000) and the indices are
## reliable (ESS = 2331)
##   - NANAThe estimation successfully converged (Rhat = 1.002) and the indices are
## reliable (ESS = 2179)
##   - NANAThe estimation successfully converged (Rhat = 0.999) and the indices are
## reliable (ESS = 2347)
##   - NANAThe estimation successfully converged (Rhat = 1.000) and the indices are
## reliable (ESS = 2200)
## 
## Following the Sequential Effect eXistence and sIgnificance Testing (SEXIT)
## framework, we report the median of the posterior distribution and its 95% CI
## (Highest Density Interval), along the probability of direction (pd), the
## probability of significance and the probability of being large. The thresholds
## beyond which the effect is considered as significant (i.e., non-negligible) and
## large are |0.05| and |0.30|. Convergence and stability of the Bayesian sampling
## has been assessed using R-hat, which should be below 1.01 (Vehtari et al.,
## 2019), and Effective Sample Size (ESS), which should be greater than 1000
## (Burkner, 2017). and We fitted a Bayesian poisson mixed model (estimated using
## MCMC sampling with 3 chains of 5000 iterations and a warmup of 1000) to predict
## richness with lat (formula: richness ~ assessment.method * scale(lat, scale =
## FALSE)). The model included site.plot as random effects (formula: list(~1 |
## site.plot:site, ~1 | site)). Priors over parameters were set as NA (NA)
## distributions. The model's explanatory power is substantial (R2 = 0.82, 95% CI
## [0.77, 0.85]) and the part related to the fixed effects alone (marginal R2) is
## of 0.80 (95% CI [0.61, 0.84]).  Within this model:
## 
##   - The effect of b Intercept (Median = 1.91, 95% CI [1.55, 2.24]) has a 100.00%
## probability of being positive (> 0), 100.00% of being significant (> 0.05), and
## 100.00% of being large (> 0.30). The estimation successfully converged (Rhat =
## 1.000) and the indices are reliable (ESS = 2331)
##   - The effect of b assessment methodfunnel (Median = -0.02, 95% CI [-0.25,
## 0.21]) has a 58.83% probability of being negative (< 0), 40.54% of being
## significant (< -0.05), and 0.92% of being large (< -0.30). The estimation
## successfully converged (Rhat = 1.002) and the indices are reliable (ESS = 2179)
##   - The effect of b assessment methodincidentals (Median = -0.91, 95% CI [-1.24,
## -0.61]) has a 100.00% probability of being negative (< 0), 100.00% of being
## significant (< -0.05), and 100.00% of being large (< -0.30). The estimation
## successfully converged (Rhat = 0.999) and the indices are reliable (ESS = 2347)
##   - The effect of b assessment methodspotlighting (Median = -1.11, 95% CI [-1.45,
## -0.78]) has a 100.00% probability of being negative (< 0), 100.00% of being
## significant (< -0.05), and 100.00% of being large (< -0.30). The estimation
## successfully converged (Rhat = 1.000) and the indices are reliable (ESS = 2200)
##   - The effect of b assessment methodcoverboard (Median = -1.57, 95% CI [-2.01,
## -1.17]) has a 100.00% probability of being negative (< 0), 100.00% of being
## significant (< -0.05), and 100.00% of being large (< -0.30). The estimation
## successfully converged (Rhat = 1.000) and the indices are reliable (ESS = 2048)
##   - The effect of b assessment methodcamera (Median = -2.48, 95% CI [-3.09,
## -1.94]) has a 100.00% probability of being negative (< 0), 100.00% of being
## significant (< -0.05), and 100.00% of being large (< -0.30). The estimation
## successfully converged (Rhat = 1.003) and the indices are reliable (ESS = 1697)
##   - The effect of b scalelatscaleEQFALSE (Median = 0.07, 95% CI [0.02, 0.12]) has
## a 99.54% probability of being positive (> 0), 84.58% of being significant (>
## 0.05), and 0.00% of being large (> 0.30). The estimation successfully converged
## (Rhat = 1.000) and the indices are reliable (ESS = 2277)
##   - The interaction effect of scalelatscaleEQFALSE on b assessment methodfunnel
## (Median = 2.43e-03, 95% CI [-0.03, 0.04]) has a 55.33% probability of being
## positive (> 0), 0.38% of being significant (> 0.05), and 0.00% of being large
## (> 0.30). The estimation successfully converged (Rhat = 1.000) and the indices
## are reliable (ESS = 2132)
##   - The interaction effect of scalelatscaleEQFALSE on b assessment
## methodincidentals (Median = 0.04, 95% CI [3.81e-04, 0.09]) has a 97.58%
## probability of being positive (> 0), 40.12% of being significant (> 0.05), and
## 0.00% of being large (> 0.30). The estimation successfully converged (Rhat =
## 1.000) and the indices are reliable (ESS = 2171)
##   - The interaction effect of scalelatscaleEQFALSE on b assessment
## methodspotlighting (Median = 0.04, 95% CI [-3.29e-03, 0.09]) has a 96.46%
## probability of being positive (> 0), 39.71% of being significant (> 0.05), and
## 0.00% of being large (> 0.30). The estimation successfully converged (Rhat =
## 0.999) and the indices are reliable (ESS = 2334)
##   - The interaction effect of scalelatscaleEQFALSE on b assessment
## methodcoverboard (Median = 0.05, 95% CI [-0.01, 0.11]) has a 94.21% probability
## of being positive (> 0), 45.88% of being significant (> 0.05), and 0.00% of
## being large (> 0.30). The estimation successfully converged (Rhat = 1.002) and
## the indices are reliable (ESS = 1302)
##   - The interaction effect of scalelatscaleEQFALSE on b assessment methodcamera
## (Median = -0.03, 95% CI [-0.11, 0.05]) has a 75.71% probability of being
## negative (< 0), 30.63% of being significant (< -0.05), and 0.00% of being large
## (< -0.30). The estimation successfully converged (Rhat = 1.001) and the indices
## are reliable (ESS = 1663)
##   - NANAThe estimation successfully converged (Rhat = 1.000) and the indices are
## reliable (ESS = 2331)
##   - NANAThe estimation successfully converged (Rhat = 1.002) and the indices are
## reliable (ESS = 2179)
##   - NANAThe estimation successfully converged (Rhat = 0.999) and the indices are
## reliable (ESS = 2347)
##   - NANAThe estimation successfully converged (Rhat = 1.000) and the indices are
## reliable (ESS = 2200)
## 
## Following the Sequential Effect eXistence and sIgnificance Testing (SEXIT)
## framework, we report the median of the posterior distribution and its 95% CI
## (Highest Density Interval), along the probability of direction (pd), the
## probability of significance and the probability of being large. The thresholds
## beyond which the effect is considered as significant (i.e., non-negligible) and
## large are |0.05| and |0.30|. Convergence and stability of the Bayesian sampling
## has been assessed using R-hat, which should be below 1.01 (Vehtari et al.,
## 2019), and Effective Sample Size (ESS), which should be greater than 1000
## (Burkner, 2017).

5 Survey Effort

Species accumulation curves

5.1 Prepare data

Merged duplicate rows for duplicate observations and transformed the dataset to a wide format.

reptile_community <- reptile_data %>% 
  select(site, date, assessment.method,scientific.name) %>% #selected relevant grouping variables
  group_by(across(everything())) %>% #groups by all available columns
  mutate(number = n()) %>% #created a numbers column that counts the number of duplicate observations
  ungroup() %>% 
  unique() %>% #merged the duplicate rows
  pivot_wider(names_from = "scientific.name", #transformed dataset from long to wide format
              values_from = "number",
              values_fill = list(number=0)) %>% #replaced NAs with 0
  arrange(site)

Add a category for the total richness.

result.i <- vector("list",length(unique(reptile_community$site))) #created an empty list that was filled as the loop ran

for(i in 1:length(unique(reptile_community$site))){ #looped over each study site
  site.i <- reptile_community[reptile_community$site == unique(reptile_community$site)[i],] #subset to the site
  
  result.a <- vector("list",length(unique(site.i$date))) #created an empty list to be filled by each date
  for(a in 1:length(unique(site.i$date))){ #looped over each date
    
    
    date.a <- site.i[site.i$date == unique(site.i$date)[a],] #subset to the date
    
    meta.a <- cbind.data.frame(date.a$site[1],date.a$date[1],c("total"))
    
    date.a <- date.a %>% select(where(is.numeric)) #removed first 3 columns of metadata and only keeps those with numeric data i.e. species columns
    
    total.a <- cbind.data.frame(meta.a,rbind.data.frame(colSums(date.a))) #calculated column sums
    
    colnames(total.a) <- colnames(reptile_community)
    
    result.a[[a]] <- total.a} #added method results to list
  
  result.i[[i]] <- do.call("rbind.data.frame",result.a) #compressed list into data frame and add to the result.i list
} #end loop

result.i <- do.call("rbind.data.frame",result.i)

reptile_community2 <- rbind.data.frame(reptile_community, result.i)

Add a category for the combined pitfall and funnel richness.

result.j <- vector("list",length(unique(reptile_community$site))) #created an empty list that was filled as the loop ran

for(i in 1:length(unique(reptile_community$site))){ #looped over each study site
  site.i <- reptile_community[reptile_community$site == unique(reptile_community$site)[i],] #subset to the site
  
  result.a <- vector("list",length(unique(site.i$date))) #created an empty list to be filled by each date
  for(a in 1:length(unique(site.i$date))){ #looped over each date
    
    
    date.a <- site.i[site.i$date == unique(site.i$date)[a],] %>% 
      filter(assessment.method %in% c("funnel", "pitfall"))
    
    meta.a <- cbind.data.frame(date.a$site[1],date.a$date[1],c("pitfunnel"))
    
    date.a <- date.a %>% select(where(is.numeric)) #removed first 3 columns of metadata and only keeps those with numeric data i.e. species columns
    
    total.a <- cbind.data.frame(meta.a,rbind.data.frame(colSums(date.a))) #calculated column sums
    
    colnames(total.a) <- colnames(reptile_community)
    
    result.a[[a]] <- total.a} #added method results to list
  
  result.j[[i]] <- do.call("rbind.data.frame",result.a) #compressed list into data frame and add to the result.i list
} #end loop

result.j <- do.call("rbind.data.frame",result.j)

reptile_community2 <- rbind.data.frame(reptile_community2, result.j) %>% 
  drop_na()

5.2 Loop

Created a loop that applied specaccum() to all methods across all sites. The output were values for richness of each method at each site over the course of the survey.

# Created a data frame of zeros with 30 rows and the same number of columns as the total number of species.
extra.rows <- data.frame(matrix(NA, nrow = 30, ncol = (ncol(reptile_community2)))) %>% 
  replace(is.na(.), 0) %>% 
  set_names(names(reptile_community2)) %>% 
  select(-(1:3))

result.i <- vector("list",length(unique(reptile_community2$site))) #created an empty list that was filled as the loop ran

set.seed(8) #set seed for reproducibility
for(i in 1:length(unique(reptile_community2$site))){ #looped over each study site
  site.i <- reptile_community2[reptile_community2$site == unique(reptile_community2$site)[i],] #subset to the site
  
  dates.i <- ifelse(unique(site.i$site) %in% c("Tarcutta", "Undara", "Wambiana", "Rinyirru"), 28, 21) #manual addition of dates depending on site to avoid any issues from 0 animals being detected by any method on a given day 
  
  result.a <- vector("list",length(unique(site.i$assessment.method))) #created an empty list to be filled by each method
  for(a in 1:length(unique(site.i$assessment.method))){ #looped over each method
    
    
    method.a <- site.i[site.i$assessment.method == unique(site.i$assessment.method)[a],] #subset to the method
    
    if(nrow(method.a) > 1){ #only proceeded if detections occurred on more than 1 day for specaccum() to work properly
      sampling.a <- method.a$assessment.method[1] #saved the name of the method
      
      method.a <- method.a %>% select(where(is.numeric)) #removed first 3 columns of metadata and only keeps those with numeric data i.e. species columns
      
      if(nrow(method.a)!=dates.i){ #if there were missing days (i.e., days when nothing was found, use the extra.rows object to add rows of zeros)
        method.a <- rbind.data.frame(method.a,extra.rows[1:(dates.i-nrow(method.a)),])}
      
      accum.a <- specaccum(method.a,"random") #calculated data
      
      #created data frame of metadata, richness, and standard deviation
      accum.a <- cbind.data.frame(rep(site.i$site[1],nrow(method.a)),rep(sampling.a,nrow(method.a)),accum.a$richness,accum.a$sd, 1:nrow(method.a))
      colnames(accum.a) <- c("site","assessment.method","richness","sd", "day")
      
      accum.a$lower.ci <- accum.a$richness-qnorm(0.975)*accum.a$sd/sqrt(100) #calculated lower 95% CI
      accum.a$upper.ci <- accum.a$richness+qnorm(0.975)*accum.a$sd/sqrt(100) #calculated upper 95% CI
      
      result.a[[a]] <- accum.a}} #added method results to list
  
  result.i[[i]] <- do.call("rbind.data.frame",result.a) #compressed list into data frame and add to the result.i list
} #end loop

Transformed resulting list to a data frame.

reptiles_wide.result <- do.call("rbind.data.frame",result.i) %>% #compressed result.i list into data frame
mutate(assessment.method = factor(assessment.method, levels = c("pitfall",
                                                                "funnel",
                                                                "incidentals",
                                                                "spotlighting",
                                                                "cover board",
                                                                "camera",
                                                                "total",
                                                                "pitfunnel")),
         site = factor(site, levels = c("Rinyirru", "Undara", "Wambiana", "Mourachan",
                                        "Duval", "Tarcutta")))

5.3 Visualisation

Plot of rarefaction curves for each method split by sites.

(specaccum_reptiles <- ggplot(reptiles_wide.result, aes(x = day, y = richness, col = assessment.method)) + 
  geom_ribbon(aes(ymin = lower.ci, ymax = upper.ci,fill=after_scale(alpha(colour, 0.3))),
              linetype = 0.1) +
  geom_vline(xintercept=c(7,14,21, 28), linetype="dotted", colour = "black") +
  geom_line(aes(group = assessment.method)) +
  my.theme() +
  facet_wrap(~site) +
  theme(panel.border = element_rect(fill = NA, color = "black", linewidth = 1.5),
        panel.grid.major.y = element_line("lightgrey", linewidth = 0.2, linetype = "solid"),
        strip.background = element_rect(fill = "lightgrey"),
        axis.title = element_text(size = 22),
        legend.title = element_text(size = 20),
        legend.text = element_text(size = 20),
        legend.position = "bottom") +
  scale_y_continuous(expand = expansion(mult = c(0, 0.07)), breaks = seq(0, 45, by = 5),
                     name = "Species Richness") +
  scale_x_continuous(breaks = seq(0, 28, by = 7),
                     name = "Survey Effort (Days)") +
  scale_colour_manual(values = c("#FF8300","#D14103","#0CC170","black",
                                 "#4E84C4","#8348D8","#FBA6EA","#E8BB5A"),
                      name = "",
                      labels = c("Pitfall Trap","Funnel Trap","Incidental",
                                 "Spotlighting","Arboreal Cover Board", "Camera Trap",
                                 "Total Richness", "Pit + Funnel")))

6 Community composition

6.1 Prepare data

reptile_community3 <- reptile_data %>% 
  filter(!recapture %in% c("y")) %>%  
  select(site, plot, assessment.method,scientific.name) %>% #selected relevant grouping variables
  group_by(across(everything())) %>% #groups by all available columns
  mutate(number = n()) %>% #created a numbers column that counts the number of duplicate observations
  ungroup() %>% 
  unique() %>% #merged the duplicate rows
  pivot_wider(names_from = "scientific.name", #transformed dataset from long to wide format
              values_from = "number",
              values_fill = list(number=0)) %>% #replaced NAs with 0
  arrange(site) %>% 
  mutate(assessment.method = factor(assessment.method))

duv <- reptile_community3 %>% filter(site=="Duval") %>% select(where(~ any(. != 0)))
mou <- reptile_community3 %>% filter(site=="Mourachan") %>% select(where(~ any(. != 0)))
rin <- reptile_community3 %>% filter(site=="Rinyirru") %>% select(where(~ any(. != 0)))
tar <- reptile_community3 %>% filter(site=="Tarcutta") %>% select(where(~ any(. != 0)))
und <- reptile_community3 %>% filter(site=="Undara") %>% select(where(~ any(. != 0)))
wam <- reptile_community3 %>% filter(site=="Wambiana") %>% select(where(~ any(. != 0)))
all <- reptile_community3 %>% select(where(~ any(. != 0)), -"Chelodina longicollis") %>% filter(rowSums(.[,4:ncol(.)]) > 0)

#Function decostand() standardises proportions (method = "total") by rows (MARGIN = 1)
rep_com_bray_duv <- duv %>%
  select(where(is.numeric)) %>%
  decostand(method="total", MARGIN = 1)
rep_com_bray_mou <- mou %>%
  select(where(is.numeric)) %>%
  decostand(method="total", MARGIN = 1)
rep_com_bray_rin <- rin %>%
  select(where(is.numeric)) %>%
  decostand(method="total", MARGIN = 1)
rep_com_bray_tar <- tar %>%
  select(where(is.numeric)) %>%
  decostand(method="total", MARGIN = 1)
rep_com_bray_und <- und %>%
  select(where(is.numeric)) %>%
  decostand(method="total", MARGIN = 1)
rep_com_bray_wam <- wam %>%
  select(where(is.numeric)) %>%
  decostand(method="total", MARGIN = 1)
rep_com_bray_all <- all %>%
  select(where(is.numeric)) %>%
  decostand(method="total", MARGIN = 1)

#Function decostand() standardises presence/absence (method = "pa") by rows (MARGIN = 1)
rep_com_jacc_duv <- duv %>%
  select(where(is.numeric)) %>%
  decostand(method="pa", MARGIN = 1)
rep_com_jacc_mou <- mou %>%
  select(where(is.numeric)) %>%
  decostand(method="pa", MARGIN = 1)
rep_com_jacc_rin <- rin %>%
  select(where(is.numeric)) %>%
  decostand(method="pa", MARGIN = 1)
rep_com_jacc_tar <- tar %>%
  select(where(is.numeric)) %>%
  decostand(method="pa", MARGIN = 1)
rep_com_jacc_und <- und %>%
  select(where(is.numeric)) %>%
  decostand(method="pa", MARGIN = 1)
rep_com_jacc_wam <- wam %>%
  select(where(is.numeric)) %>%
  decostand(method="pa", MARGIN = 1)
rep_com_jacc_all <- all %>%
  select(where(is.numeric)) %>%
  decostand(method="pa", MARGIN = 1)

6.2 NMDS Ordination

6.2.1 Bray-Curtis dissimilarity

all_nmds_bray <-  metaMDS(rep_com_bray_all, distance="bray", k=3,trymax=100, noshare=0.1)
rin_nmds_bray <-  metaMDS(rep_com_bray_rin, distance="bray", k=2,trymax=100)
und_nmds_bray <-  metaMDS(rep_com_bray_und, distance="bray", k=2,trymax=100)
wam_nmds_bray <-  metaMDS(rep_com_bray_wam, distance="bray", k=2,trymax=100)
mou_nmds_bray <-  metaMDS(rep_com_bray_mou, distance="bray", k=2,trymax=1000)

#removed due to insufficient data
duv_nmds_bray <-  metaMDS(rep_com_bray_duv, distance="bray", k=2,trymax=100)

## Warning in metaMDS(rep_com_bray_duv, distance = "bray", k = 2, trymax = 100):
## stress is (nearly) zero: you may have insufficient data

tar_nmds_bray <-  metaMDS(rep_com_bray_tar, distance="bray", k=2,trymax=100)

## Warning in metaMDS(rep_com_bray_tar, distance = "bray", k = 2, trymax = 100):
## stress is (nearly) zero: you may have insufficient data

6.2.2 Jaccard dissimilarity

all_nmds_jacc <-  metaMDS(rep_com_jacc_all, distance="jaccard", k=2,trymax=100, noshare=0.1)
rin_nmds_jacc <-  metaMDS(rep_com_jacc_rin, distance="jaccard", k=2,trymax=100)
und_nmds_jacc <-  metaMDS(rep_com_jacc_und, distance="jaccard", k=2,trymax=100)
wam_nmds_jacc <-  metaMDS(rep_com_jacc_wam, distance="jaccard", k=2,trymax=100)
mou_nmds_jacc <-  metaMDS(rep_com_jacc_mou, distance="jaccard", k=2,trymax=100)

#removed due to insufficient data
duv_nmds_jacc <-  metaMDS(rep_com_jacc_duv, distance="jaccard", k=2,trymax=100)

## Warning in metaMDS(rep_com_jacc_duv, distance = "jaccard", k = 2, trymax =
## 100): stress is (nearly) zero: you may have insufficient data

tar_nmds_jacc <-  metaMDS(rep_com_jacc_tar, distance="jaccard", k=2,trymax=100)

## Warning in metaMDS(rep_com_jacc_tar, distance = "jaccard", k = 2, trymax =
## 100): stress is (nearly) zero: you may have insufficient data

6.3 Visualisation

6.3.1 Bray-Curtis dissimilarity

all.methods <- all_nmds_bray$points
all.species <- as.data.frame(all_nmds_bray$species) %>% 
  mutate(species = row.names(.))
all2 <- all[,1:3]
rep_com_bray_all2 <- cbind.data.frame(all2, all.methods)


gg <- merge(rep_com_bray_all2,aggregate(cbind(mean.x=MDS1,mean.y=MDS2)~assessment.method,rep_com_bray_all2,mean),by="assessment.method") %>% 
  mutate(assessment.method = factor(assessment.method, levels = c("pitfall","funnel","incidentals","spotlighting","cover board","camera","total")))

(mds.all.plot.bray.centroid <- ggplot(gg, aes(MDS1,MDS2,color=assessment.method)) +
  geom_point(size=3) +
  geom_point(aes(x=mean.x,y=mean.y),size=5) +
  scale_colour_manual(values = c("#FF8300", "#D14103","#0CC170","black","#4E84C4","#8348D8","#FBA6EA"),
                      name = "",
                      labels = c("Pitfall Trap","Funnel Trap","Incidental",
                                 "Spotlighting","Arboreal Cover Board",
                                 "Camera Trap")) +
  geom_segment(aes(x=mean.x, y=mean.y, xend=MDS1, yend=MDS2), alpha = 0.2, linewidth = 1.5) +
  my.theme() +
    theme(legend.position = "bottom"))

rin.methods <- rin_nmds_bray$points
rin.species <- as.data.frame(rin_nmds_bray$species) %>% 
  mutate(species = row.names(.))
rin2 <- rin[,1:3]
rep_com_bray_rin2 <- cbind.data.frame(rin2, rin.methods)


gg <- merge(rep_com_bray_rin2,aggregate(cbind(mean.x=MDS1,mean.y=MDS2)~assessment.method,rep_com_bray_rin2,mean),by="assessment.method") %>% 
  mutate(assessment.method = factor(assessment.method, levels = c("pitfall","funnel","incidentals","spotlighting","cover board","camera","total")))

(mds.rin.plot.bray.centroid <- ggplot(gg, aes(MDS1,MDS2,color=assessment.method)) +
  geom_point(size=3) +
  geom_point(aes(x=mean.x,y=mean.y),size=5) +
  scale_colour_manual(values = c("#FF8300", "#D14103","#0CC170","black","#4E84C4","#8348D8","#FBA6EA"),
                      name = "",
                      labels = c("Pitfall Trap","Funnel Trap","Incidental",
                                 "Spotlighting","Arboreal Cover Board",
                                 "Camera Trap")) +
  geom_segment(aes(x=mean.x, y=mean.y, xend=MDS1, yend=MDS2), alpha = 0.2, linewidth = 1.5) +
  my.theme() +
    theme(legend.position = "bottom"))

und.methods <- und_nmds_bray$points
und.species <- as.data.frame(und_nmds_bray$species) %>% 
  mutate(species = row.names(.))
und2 <- und[,1:3]
rep_com_bray_und2 <- cbind.data.frame(und2, und.methods)


gg <- merge(rep_com_bray_und2,aggregate(cbind(mean.x=MDS1,mean.y=MDS2)~assessment.method,rep_com_bray_und2,mean),by="assessment.method") %>% 
  mutate(assessment.method = factor(assessment.method, levels = c("pitfall","funnel","incidentals","spotlighting","cover board","camera","total")))

(mds.und.plot.bray.centroid <- ggplot(gg, aes(MDS1,MDS2,color=assessment.method)) +
  geom_point(size=3) +
  geom_point(aes(x=mean.x,y=mean.y),size=5) +
  scale_colour_manual(values = c("#FF8300", "#D14103","#0CC170","black","#4E84C4","#8348D8","#FBA6EA"),
                      name = "",
                      labels = c("Pitfall Trap","Funnel Trap","Incidental",
                                 "Spotlighting","Arboreal Cover Board",
                                 "Camera Trap")) +
  geom_segment(aes(x=mean.x, y=mean.y, xend=MDS1, yend=MDS2), alpha = 0.2, linewidth = 1.5) +
  my.theme() +
    theme(legend.position = "bottom"))

wam.methods <- wam_nmds_bray$points
wam.species <- as.data.frame(wam_nmds_bray$species) %>% 
  mutate(species = row.names(.))
wam2 <- wam[,1:3]
rep_com_bray_wam2 <- cbind.data.frame(wam2, wam.methods)


gg <- merge(rep_com_bray_wam2,aggregate(cbind(mean.x=MDS1,mean.y=MDS2)~assessment.method,rep_com_bray_wam2,mean),by="assessment.method") %>% 
  mutate(assessment.method = factor(assessment.method, levels = c("pitfall","funnel","incidentals","spotlighting","cover board","camera","total")))

(mds.wam.plot.bray.centroid <- ggplot(gg, aes(MDS1,MDS2,color=assessment.method)) +
  geom_point(size=3) +
  geom_point(aes(x=mean.x,y=mean.y),size=5) +
  scale_colour_manual(values = c("#FF8300", "#D14103","#0CC170","black","#4E84C4","#8348D8","#FBA6EA"),
                      name = "",
                      labels = c("Pitfall Trap","Funnel Trap","Incidental",
                                 "Spotlighting","Arboreal Cover Board",
                                 "Camera Trap")) +
  geom_segment(aes(x=mean.x, y=mean.y, xend=MDS1, yend=MDS2), alpha = 0.2, linewidth = 1.5) +
  my.theme() +
    theme(legend.position = "bottom"))

mou.methods <- mou_nmds_bray$points
mou.species <- as.data.frame(mou_nmds_bray$species) %>% 
  mutate(species = row.names(.))
mou2 <- mou[,1:3]
rep_com_bray_mou2 <- cbind.data.frame(mou2, mou.methods)


gg <- merge(rep_com_bray_mou2,aggregate(cbind(mean.x=MDS1,mean.y=MDS2)~assessment.method,rep_com_bray_mou2,mean),by="assessment.method") %>% 
  mutate(assessment.method = factor(assessment.method, levels = c("pitfall","funnel","incidentals","spotlighting","cover board","camera","total")))

(mds.mou.plot.bray.centroid <- ggplot(gg, aes(MDS1,MDS2,color=assessment.method)) +
  geom_point(size=3) +
  geom_point(aes(x=mean.x,y=mean.y),size=5) +
  scale_colour_manual(values = c("#FF8300", "#D14103","#0CC170","black","#4E84C4","#8348D8","#FBA6EA"),
                      name = "",
                      labels = c("Pitfall Trap","Funnel Trap","Incidental",
                                 "Spotlighting","Arboreal Cover Board",
                                 "Camera Trap")) +
  geom_segment(aes(x=mean.x, y=mean.y, xend=MDS1, yend=MDS2), alpha = 0.2, linewidth = 1.5) +
  my.theme() +
    theme(legend.position = "bottom"))

(mds.bray.all <- (mds.all.plot.bray.centroid + 
  ggtitle('All sites') & theme(legend.position = "none")) +
   (mds.rin.plot.bray.centroid + 
  ggtitle('Rinyirru') & theme(legend.position = "none")) +
   (mds.und.plot.bray.centroid + 
  ggtitle('Undara') & theme(legend.position = "none")) +
   (mds.wam.plot.bray.centroid + 
  ggtitle('Wambiana') & theme(legend.position = "none")) +
   (mds.mou.plot.bray.centroid + 
  ggtitle('Mourachan') & theme(legend.position = "none")) + 
   plot_annotation(tag_levels = "A", tag_suffix = ')') + 
   theme(legend.position = c(2,0.65), legend.text = element_text(size = 18)))

6.3.2 Jaccard dissimilarity

all.methods.jacc <- all_nmds_jacc$points
all.species.jacc <- as.data.frame(all_nmds_jacc$species) %>% 
  mutate(species = row.names(.))
all2 <- all[,1:3]
rep_com_jacc_all2 <- cbind.data.frame(all2, all.methods.jacc)


gg <- merge(rep_com_jacc_all2,aggregate(cbind(mean.x=MDS1,mean.y=MDS2)~assessment.method,rep_com_jacc_all2,mean),by="assessment.method") %>% 
  mutate(assessment.method = factor(assessment.method, levels = c("pitfall","funnel","incidentals","spotlighting","cover board","camera","total")))

(mds.all.plot.jacc.centroid <- ggplot(gg, aes(MDS1,MDS2,color=assessment.method)) +
  geom_point(size=3) +
  geom_point(aes(x=mean.x,y=mean.y),size=5) +
  scale_colour_manual(values = c("#FF8300", "#D14103","#0CC170","black","#4E84C4","#8348D8","#FBA6EA"),
                      name = "",
                      labels = c("Pitfall Trap","Funnel Trap","Incidental",
                                 "Spotlighting","Arboreal Cover Board",
                                 "Camera Trap")) +
  geom_segment(aes(x=mean.x, y=mean.y, xend=MDS1, yend=MDS2), alpha = 0.2, linewidth = 1.5) +
  my.theme() +
    theme(legend.position = "bottom"))

rin.methods <- rin_nmds_jacc$points
rin.species <- as.data.frame(rin_nmds_jacc$species) %>% 
  mutate(species = row.names(.))
rin2 <- rin[,1:3]
rep_com_jacc_rin2 <- cbind.data.frame(rin2, rin.methods)


gg <- merge(rep_com_jacc_rin2,aggregate(cbind(mean.x=MDS1,mean.y=MDS2)~assessment.method,rep_com_jacc_rin2,mean),by="assessment.method") %>% 
  mutate(assessment.method = factor(assessment.method, levels = c("pitfall","funnel","incidentals","spotlighting","cover board","camera","total")))

(mds.rin.plot.jacc.centroid <- ggplot(gg, aes(MDS1,MDS2,color=assessment.method)) +
  geom_point(size=3) +
  geom_point(aes(x=mean.x,y=mean.y),size=5) +
  scale_colour_manual(values = c("#FF8300", "#D14103","#0CC170","black","#4E84C4","#8348D8","#FBA6EA"),
                      name = "",
                      labels = c("Pitfall Trap","Funnel Trap","Incidental",
                                 "Spotlighting","Arboreal Cover Board",
                                 "Camera Trap")) +
  geom_segment(aes(x=mean.x, y=mean.y, xend=MDS1, yend=MDS2), alpha = 0.2, linewidth = 1.5) +
  my.theme() +
    theme(legend.position = "bottom"))

und.methods <- und_nmds_jacc$points
und.species <- as.data.frame(und_nmds_jacc$species) %>% 
  mutate(species = row.names(.))
und2 <- und[,1:3]
rep_com_jacc_und2 <- cbind.data.frame(und2, und.methods)


gg <- merge(rep_com_jacc_und2,aggregate(cbind(mean.x=MDS1,mean.y=MDS2)~assessment.method,rep_com_jacc_und2,mean),by="assessment.method") %>% 
  mutate(assessment.method = factor(assessment.method, levels = c("pitfall","funnel","incidentals","spotlighting","cover board","camera","total")))

(mds.und.plot.jacc.centroid <- ggplot(gg, aes(MDS1,MDS2,color=assessment.method)) +
  geom_point(size=3) +
  geom_point(aes(x=mean.x,y=mean.y),size=5) +
  scale_colour_manual(values = c("#FF8300", "#D14103","#0CC170","black","#4E84C4","#8348D8","#FBA6EA"),
                      name = "",
                      labels = c("Pitfall Trap","Funnel Trap","Incidental",
                                 "Spotlighting","Arboreal Cover Board",
                                 "Camera Trap")) +
  geom_segment(aes(x=mean.x, y=mean.y, xend=MDS1, yend=MDS2), alpha = 0.2, linewidth = 1.5) +
  my.theme() +
    theme(legend.position = "bottom"))

wam.methods <- wam_nmds_jacc$points
wam.species <- as.data.frame(wam_nmds_jacc$species) %>% 
  mutate(species = row.names(.))
wam2 <- wam[,1:3]
rep_com_jacc_wam2 <- cbind.data.frame(wam2, wam.methods)


gg <- merge(rep_com_jacc_wam2,aggregate(cbind(mean.x=MDS1,mean.y=MDS2)~assessment.method,rep_com_jacc_wam2,mean),by="assessment.method") %>% 
  mutate(assessment.method = factor(assessment.method, levels = c("pitfall","funnel","incidentals","spotlighting","cover board","camera","total")))

(mds.wam.plot.jacc.centroid <- ggplot(gg, aes(MDS1,MDS2,color=assessment.method)) +
  geom_point(size=3) +
  geom_point(aes(x=mean.x,y=mean.y),size=5) +
  scale_colour_manual(values = c("#FF8300", "#D14103","#0CC170","black","#4E84C4","#8348D8","#FBA6EA"),
                      name = "",
                      labels = c("Pitfall Trap","Funnel Trap","Incidental",
                                 "Spotlighting","Arboreal Cover Board",
                                 "Camera Trap")) +
  geom_segment(aes(x=mean.x, y=mean.y, xend=MDS1, yend=MDS2), alpha = 0.2, linewidth = 1.5) +
  my.theme() +
    theme(legend.position = "bottom"))

mou.methods <- mou_nmds_jacc$points
mou.species <- as.data.frame(mou_nmds_jacc$species) %>% 
  mutate(species = row.names(.))
mou2 <- mou[,1:3]
rep_com_jacc_mou2 <- cbind.data.frame(mou2, mou.methods)


gg <- merge(rep_com_jacc_mou2,aggregate(cbind(mean.x=MDS1,mean.y=MDS2)~assessment.method,rep_com_jacc_mou2,mean),by="assessment.method") %>% 
  mutate(assessment.method = factor(assessment.method, levels = c("pitfall","funnel","incidentals","spotlighting","cover board","camera","total")))

(mds.mou.plot.jacc.centroid <- ggplot(gg, aes(MDS1,MDS2,color=assessment.method)) +
  geom_point(size=3) +
  geom_point(aes(x=mean.x,y=mean.y),size=5) +
  scale_colour_manual(values = c("#FF8300", "#D14103","#0CC170","black","#4E84C4","#8348D8","#FBA6EA"),
                      name = "",
                      labels = c("Pitfall Trap","Funnel Trap","Incidental",
                                 "Spotlighting","Arboreal Cover Board",
                                 "Camera Trap")) +
  geom_segment(aes(x=mean.x, y=mean.y, xend=MDS1, yend=MDS2), alpha = 0.2, linewidth = 1.5) +
  my.theme() +
    theme(legend.position = "bottom"))

(mds.jacc.all <- (mds.all.plot.jacc.centroid + 
  ggtitle('All sites') & theme(legend.position = "none")) +
   (mds.rin.plot.jacc.centroid + 
  ggtitle('Rinyirru') & theme(legend.position = "none")) +
   (mds.und.plot.jacc.centroid + 
  ggtitle('Undara') & theme(legend.position = "none")) +
   (mds.wam.plot.jacc.centroid + 
  ggtitle('Wambiana') & theme(legend.position = "none")) +
   (mds.mou.plot.jacc.centroid + 
  ggtitle('Mourachan') & theme(legend.position = "none")) + 
   plot_annotation(tag_levels = "A", tag_suffix = ')') + 
   theme(legend.position = c(2,0.65), legend.text = element_text(size = 18)))

6.4 Investigation

6.5 Adonis

6.5.1 Bray-Curtis dissimilarity

all_b <- all %>% mutate(assessment.method = factor(assessment.method))
all.dist <- vegdist(all[4:ncol(all)], 'bray')
(all.adonis <- adonis2(all.dist ~ assessment.method, data=all_b))

## Permutation test for adonis under reduced model
## Terms added sequentially (first to last)
## Permutation: free
## Number of permutations: 999
## 
## adonis2(formula = all.dist ~ assessment.method, data = all_b)
##                    Df SumOfSqs      R2      F Pr(>F)    
## assessment.method   5   10.309 0.21227 5.5511  0.001 ***
## Residual          103   38.257 0.78773                  
## Total             108   48.566 1.00000                  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

#Permutation test: significant difference between assessment methods for reptile communities.

#Let's which method is different from which
(adonis.methods.bray <- EcolUtils::adonis.pair(all.dist, all$assessment.method))

##                     combination SumsOfSqs   MeanSqs    F.Model         R2
## 1        camera <-> cover board 2.8879066 2.8879066  9.3629077 0.27247135
## 2             camera <-> funnel 2.7328065 2.7328065  7.5459644 0.19081503
## 3        camera <-> incidentals 2.4035118 2.4035118  6.8296694 0.20803345
## 4            camera <-> pitfall 2.7403269 2.7403269  7.4979872 0.18983213
## 5       camera <-> spotlighting 3.1100425 3.1100425 11.2489845 0.31912932
## 6        cover board <-> funnel 2.6722775 2.6722775  6.9302710 0.15088679
## 7   cover board <-> incidentals 1.5522584 1.5522584  4.0656878 0.10968872
## 8       cover board <-> pitfall 2.2871233 2.2871233  5.8898007 0.13120577
## 9  cover board <-> spotlighting 1.0719637 1.0719637  3.2952071 0.09608360
## 10       funnel <-> incidentals 1.5296767 1.5296767  3.7134502 0.08494983
## 11           funnel <-> pitfall 0.3802544 0.3802544  0.9195332 0.01959809
## 12      funnel <-> spotlighting 2.8043239 2.8043239  7.6321637 0.16725404
## 13      incidentals <-> pitfall 1.4649808 1.4649808  3.5336081 0.08116966
## 14 incidentals <-> spotlighting 1.5851769 1.5851769  4.4019111 0.12092527
## 15     pitfall <-> spotlighting 2.7086276 2.7086276  7.3160470 0.16144495
##        P.value P.value.corrected
## 1  0.000999001       0.001152693
## 2  0.000999001       0.001152693
## 3  0.000999001       0.001152693
## 4  0.000999001       0.001152693
## 5  0.000999001       0.001152693
## 6  0.000999001       0.001152693
## 7  0.000999001       0.001152693
## 8  0.000999001       0.001152693
## 9  0.003996004       0.004281433
## 10 0.000999001       0.001152693
## 11 0.496503497       0.496503497
## 12 0.000999001       0.001152693
## 13 0.000999001       0.001152693
## 14 0.000999001       0.001152693
## 15 0.000999001       0.001152693

#comparing all methods with each other
#evidence that everything but pitfall vs funnel traps capture significantly different reptile communities.

6.5.2 Jaccard dissimilarity

all_j <- all %>% mutate(assessment.method = factor(assessment.method))
all.dist2 <- vegdist(rep_com_jacc_all, 'jaccard')
(all.adonis <- adonis2(all.dist2 ~ assessment.method, data=all_j))

## Permutation test for adonis under reduced model
## Terms added sequentially (first to last)
## Permutation: free
## Number of permutations: 999
## 
## adonis2(formula = all.dist2 ~ assessment.method, data = all_j)
##                    Df SumOfSqs      R2      F Pr(>F)    
## assessment.method   5    9.069 0.18829 4.7785  0.001 ***
## Residual          103   39.098 0.81171                  
## Total             108   48.168 1.00000                  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

#Permutation test: significant difference between assessment methods for reptile communities.

#Let's which method is different from which
(adonis.methods.jacc <- EcolUtils::adonis.pair(all.dist2, all$assessment.method))

##                     combination SumsOfSqs   MeanSqs    F.Model         R2
## 1        camera <-> cover board 3.0365859 3.0365859 10.3763129 0.29331245
## 2             camera <-> funnel 2.6272329 2.6272329  7.0453213 0.18043958
## 3        camera <-> incidentals 2.3585467 2.3585467  6.5429368 0.20105551
## 4            camera <-> pitfall 2.7649371 2.7649371  7.6180333 0.19228701
## 5       camera <-> spotlighting 2.8379001 2.8379001  9.2684496 0.27859578
## 6        cover board <-> funnel 2.6169850 2.6169850  6.8014219 0.14849805
## 7   cover board <-> incidentals 1.3558707 1.3558707  3.5952112 0.09824267
## 8       cover board <-> pitfall 2.3940005 2.3940005  6.3568896 0.14015268
## 9  cover board <-> spotlighting 1.1861516 1.1861516  3.5283038 0.10218584
## 10       funnel <-> incidentals 1.0036015 1.0036015  2.3528111 0.05555265
## 11           funnel <-> pitfall 0.3502649 0.3502649  0.8346477 0.01782116
## 12      funnel <-> spotlighting 2.0596818 2.0596818  5.2045248 0.12046249
## 13      incidentals <-> pitfall 1.1301393 1.1301393  2.6998874 0.06322938
## 14 incidentals <-> spotlighting 0.5189479 0.5189479  1.3308740 0.03992917
## 15     pitfall <-> spotlighting 2.1228472 2.1228472  5.4802619 0.12604022
##        P.value P.value.corrected
## 1  0.000999001       0.001248751
## 2  0.000999001       0.001248751
## 3  0.000999001       0.001248751
## 4  0.000999001       0.001248751
## 5  0.000999001       0.001248751
## 6  0.000999001       0.001248751
## 7  0.000999001       0.001248751
## 8  0.000999001       0.001248751
## 9  0.000999001       0.001248751
## 10 0.001998002       0.002305387
## 11 0.601398601       0.601398601
## 12 0.000999001       0.001248751
## 13 0.000999001       0.001248751
## 14 0.183816184       0.196945911
## 15 0.000999001       0.001248751

#comparing all methods with each other
#evidence that everything but pitfall vs funnel traps capture significantly different reptile communities.

7 Detection probability

Detection probability between methods for reptile families (maybe also terrestrial vs arboreal)

Binary linear logistic model for the likelihood to detect a reptile of the different families for the methods across sites.

7.1 Prepare data

#Number of individuals of each species captured by each method per survey plot for every survey day.
reptile_community4 <- reptile_data %>% 
  unite(site.plot, c(site, plot), sep = ".", remove = FALSE) %>% 
  select(-plot) %>%
  select(site, site.plot, date, assessment.method, scientific.name) %>% #selected relevant grouping variables
  group_by_at(1:4) %>%
  mutate(number = n()) %>% #created a numbers column that counts the number of duplicate observations
  ungroup() %>% 
  unique() %>% #merged the duplicate rows
  pivot_wider(names_from = "scientific.name", #transformed dataset from long to wide format
              values_from = "number",
              values_fill = list(number=0)) %>% #replaced NAs with 0
  arrange(site)

#Turn abundances for each species into a binary present/absent (1/0).
rep_com_binary <- reptile_community4 %>%
  select(where(is.numeric)) %>%
  decostand(method="pa", MARGIN = 1) %>% 
  cbind(reptile_community4[,c(2,4)]) %>% 
  select(site.plot, assessment.method, everything())

#Make data frame with each method for each site.plot
all.methods <- cbind.data.frame(site.plot=rep(unique(rep_com_binary$site.plot),each=6),asssessment.method=rep(unique(rep_com_binary$assessment.method),24))

#Add merged column
all.methods$site.plot.method <- paste(all.methods$site.plot,all.methods$asssessment.method)

#Find site.plot.methods that are missing from the rep_com_binary because they never documented any species at that plot
missing <- setdiff(all.methods$site.plot.method,paste(rep_com_binary$site.plot,rep_com_binary$assessment.method))

#Make data frame of those missing values with a zero filled in for each species
missing <- cbind.data.frame(all.methods[which(all.methods$site.plot.method %in% missing),1:2],as.data.frame(matrix(0, ncol=ncol(rep_com_binary)-2, nrow=length(missing))))
colnames(missing) <- colnames(rep_com_binary)

#Add missing entries
rep_com_binary <- rep_com_binary %>% 
  bind_rows(missing)
     
#Convert to long format
rep_com_binary.long <- melt(rep_com_binary,id=c("site.plot","assessment.method")) %>% 
  rename(scientific.name = variable)

#Get a count of days when a species was present for a given method for a given plot
days.present <- rep_com_binary.long %>% 
  group_by(site.plot,assessment.method,scientific.name) %>% 
  dplyr::summarize(days.present = sum(value,na.rm=T))

#Add the survey days information (days surveyed)
survey_days <- read.csv("survey_days.csv")
days.present <- merge(days.present,survey_days,by="site.plot",all.x=T,all.y=T)

#Make a new column that is the total number of days a species was present per plot, summed across all methods and exclude plots where species was never found.
days.present <- days.present %>% 
  group_by(site.plot,scientific.name) %>% 
  mutate(count.per.site.plot = sum(days.present,na.rm=T),
         assessment.method = factor(assessment.method, levels = c("pitfall", "funnel","incidentals","spotlighting","cover board","camera"))) %>% 
  filter(count.per.site.plot > 0) %>% #Remove plots where species were never found
  select(-count.per.site.plot) %>% 
  mutate(det.prob = days.present/days) %>% #Probability of detecting a species via a given method at a given plot.
  ungroup()

This data frame now contains rows for species only for the plots where it was found but for each plot where it was found, it contains rows for each method, regardless whether that method detected it or not.

The days.present column shows the number of days when a species was detected in that plot by that method, the days column shows the number of days when that method was used at that plot and the det.prob column shows the probability of detecting a species via that method at that plot.

Include lifestyle information.

#Join with data frame that has plot and coordinate information
det.plot <- days.present %>% 
  left_join(coord)

#Lifestyles for species per plot
det.plot.groups <- det.plot %>%
  mutate(assessment.method = factor(assessment.method, levels = c("pitfall", "funnel", "incidentals",
                                                                  "spotlighting",
                                                                  "cover board","camera"))) %>%
  add_column(lifestyle = ifelse(.$scientific.name %in% c("Cryptoblepharus australis",
                                                         "Cryptoblepharus pannosus",
                                                   "Diplodactylus vittatus", "Gehyra dubia",
                                                   "Amalosia rhombifer", "Cryptoblepharus adamsi",
                                                   "Cryptoblepharus metallicus", "Oedura castelnaui",
                                                   "Cryptoblepharus virgatus", "Chlamydosaurus kingii",
                                                   "Varanus tristis", "Strophurus williamsi",
                                                   "Oedura coggeri", "Varanus scalaris",
                                                   "Egernia striolata", "Christinus marmoratus",
                                                   "Boiga irregularis", "Hoplocephalus bitorquatus"),
                                "Arboreal Species", "Ground-dwelling Species"))

7.2 Bayesian Analysis - across all methods for all reptiles

7.2.1 Priors

Defining priors for Bayesian models.

Priors for the intercept.

det.plot.groups %>% 
  filter(days.present > 0) %>% 
  summarise(median(days.present))

## # A tibble: 1 × 1
##   `median(days.present)`
##                    <dbl>
## 1                      2

#2
det.plot.groups %>% 
  filter(days.present > 0) %>%
  summarise(mad(days.present))

## # A tibble: 1 × 1
##   `mad(days.present)`
##                 <dbl>
## 1                1.48

#1.5

Priors for the slope.

sd(det.plot.groups$days.present)/apply(model.matrix(~assessment.method*lat, data = det.plot.groups), 2, sd)

##                       (Intercept)           assessment.methodfunnel 
##                               Inf                         7.2485665 
##      assessment.methodincidentals     assessment.methodspotlighting 
##                         7.2485665                         7.2485665 
##      assessment.methodcover board           assessment.methodcamera 
##                         7.2485665                         7.2485665 
##                               lat       assessment.methodfunnel:lat 
##                         0.4340015                         0.3212041 
##  assessment.methodincidentals:lat assessment.methodspotlighting:lat 
##                         0.3212041                         0.3212041 
##  assessment.methodcover board:lat       assessment.methodcamera:lat 
##                         0.3212041                         0.3212041

#4.7 <- too high, let's go for 1.5

7.2.2 Fit model

7.2.2.1 Model 1

priors1 <- prior(normal(2,1.5), class  = "Intercept") +
  prior(normal(0,1.5), class = "b") +
  prior(student_t(3,0,1.5), class = "sd")

methods.form1 <- bf(days.present ~ assessment.method*lat + offset(log(days)) + (1|site/site.plot) +
                      (1|scientific.name), family=poisson(link='log'))

methods.det.brm1 <- brm(methods.form1,
                  data = det.plot.groups,
                  prior = priors1,
                  sample_prior = "only",
                  refresh = 0,
                  chains = 3, cores = 3,
                  iter = 5000,
                  thin = 5,
                  seed = 1,
                  warmup = 1000,
                  backend = 'cmdstanr')

## Running MCMC with 3 parallel chains...
## 
## Chain 1 finished in 0.5 seconds.
## Chain 2 finished in 0.5 seconds.
## Chain 3 finished in 0.5 seconds.
## 
## All 3 chains finished successfully.
## Mean chain execution time: 0.5 seconds.
## Total execution time: 0.6 seconds.

7.2.2.1.1 Predictions

methods.det.brm1 %>% ggpredict(~assessment.method|lat) %>% plot(add.data = TRUE)

methods.det.brm1 %>% ggpredict(~lat|assessment.method) %>% plot(add.data = TRUE)

7.2.2.1.2 Prior vs Posterior

methods.det.brm1b <- methods.det.brm1 %>%
  update(sample_prior = "yes",
         refresh = 0,
         seed = 1,
         cores = 3,
         backend = "cmdstanr")

## Running MCMC with 3 parallel chains...
## 
## Chain 2 finished in 167.5 seconds.
## Chain 1 finished in 183.1 seconds.
## Chain 3 finished in 309.4 seconds.
## 
## All 3 chains finished successfully.
## Mean chain execution time: 220.0 seconds.
## Total execution time: 309.6 seconds.

7.2.2.1.3 Predictions

methods.det.brm1b %>% ggpredict(~assessment.method|lat) %>% plot(add.data = TRUE)

methods.det.brm1b %>% ggpredict(~lat|assessment.method) %>% plot(add.data = TRUE)

7.2.2.2 Model 2

priors1 <- prior(normal(2,1.5), class  = "Intercept") +
  prior(normal(0,1.5), class = "b") +
  prior(student_t(3,0,1.5), class = "sd")

methods.form2 <- bf(days.present ~ assessment.method*lat + offset(log(days)) + (1|site/site.plot) +
                      (1|scientific.name), family="negbinomial")

methods.det.brm2 <- brm(methods.form2,
                  data = det.plot.groups,
                  prior = priors1,
                  sample_prior = "only",
                  refresh = 0,
                  chains = 3, cores = 3,
                  iter = 5000,
                  thin = 5,
                  seed = 1,
                  warmup = 1000,
                  backend = 'cmdstanr')

## Running MCMC with 3 parallel chains...
## 
## Chain 3 finished in 3.0 seconds.
## Chain 2 finished in 4.3 seconds.
## Chain 1 finished in 4.5 seconds.
## 
## All 3 chains finished successfully.
## Mean chain execution time: 4.0 seconds.
## Total execution time: 4.6 seconds.

7.2.2.2.1 Predictions

methods.det.brm2 %>% ggpredict(~assessment.method|lat) %>% plot(add.data = TRUE)

methods.det.brm2 %>% ggpredict(~lat|assessment.method) %>% plot(add.data = TRUE)

7.2.2.2.2 Prior vs Posterior

methods.det.brm2b <- methods.det.brm2 %>%
  update(sample_prior = "yes",
         refresh = 0,
         seed = 1,
         cores = 3,
         backend = "cmdstanr")

## Running MCMC with 3 parallel chains...
## 
## Chain 2 finished in 47.7 seconds.
## Chain 1 finished in 64.3 seconds.
## Chain 3 finished in 73.7 seconds.
## 
## All 3 chains finished successfully.
## Mean chain execution time: 61.9 seconds.
## Total execution time: 73.9 seconds.

7.2.2.2.3 Predictions

methods.det.brm2b %>% ggpredict(~assessment.method|lat) %>% plot(add.data = TRUE)

methods.det.brm2b %>% ggpredict(~lat|assessment.method) %>% plot(add.data = TRUE)

7.2.2.3 Model 3

priors1 <- prior(normal(2,1.5), class  = "Intercept") +
  prior(normal(0,1.5), class = "b") +
  prior(student_t(3,0,1.5), class = "sd")

methods.form3 <- bf(days.present ~ assessment.method*lat + offset(log(days)) + (1|site/site.plot) +
                      (1|scientific.name), family="negbinomial2")

methods.det.brm3 <- brm(methods.form3,
                  data = det.plot.groups,
                  prior = priors1,
                  sample_prior = "only",
                  refresh = 0,
                  chains = 3, cores = 3,
                  iter = 5000,
                  thin = 5,
                  seed = 1,
                  warmup = 1000,
                  backend = 'cmdstanr')

## Running MCMC with 3 parallel chains...
## 
## Chain 1 finished in 0.5 seconds.
## Chain 2 finished in 0.5 seconds.
## Chain 3 finished in 0.5 seconds.
## 
## All 3 chains finished successfully.
## Mean chain execution time: 0.5 seconds.
## Total execution time: 0.6 seconds.

7.2.2.3.1 Predictions

methods.det.brm3 %>% ggpredict(~assessment.method|lat) %>% plot(add.data = TRUE)

methods.det.brm3 %>% ggpredict(~lat|assessment.method) %>% plot(add.data = TRUE)

7.2.2.3.2 Prior vs Posterior

methods.det.brm3b <- methods.det.brm3 %>%
  update(sample_prior = "yes",
         refresh = 0,
         seed = 1,
         cores = 3,
         backend = "cmdstanr")

## Running MCMC with 3 parallel chains...
## 
## Chain 2 finished in 51.9 seconds.
## Chain 3 finished in 52.5 seconds.
## Chain 1 finished in 53.0 seconds.
## 
## All 3 chains finished successfully.
## Mean chain execution time: 52.4 seconds.
## Total execution time: 53.1 seconds.

7.2.2.3.3 Predictions

methods.det.brm3b %>% ggpredict(~assessment.method|lat) %>% plot(add.data = TRUE)

methods.det.brm3b %>% ggpredict(~lat|assessment.method) %>% plot(add.data = TRUE)

7.2.2.4 Compare Models

(m.1b <- methods.det.brm1b %>% loo())

## Warning: Found 14 observations with a pareto_k > 0.7 in model '.'. It is
## recommended to set 'moment_match = TRUE' in order to perform moment matching
## for problematic observations.

## 
## Computed from 2400 by 2070 log-likelihood matrix
## 
##          Estimate    SE
## elpd_loo  -3054.4 132.5
## p_loo       286.2  25.7
## looic      6108.8 265.0
## ------
## Monte Carlo SE of elpd_loo is NA.
## 
## Pareto k diagnostic values:
##                          Count Pct.    Min. n_eff
## (-Inf, 0.5]   (good)     2037  98.4%   24        
##  (0.5, 0.7]   (ok)         19   0.9%   14        
##    (0.7, 1]   (bad)        11   0.5%   5         
##    (1, Inf)   (very bad)    3   0.1%   3         
## See help('pareto-k-diagnostic') for details.

(m.2b <- methods.det.brm2b %>% loo())

## Warning: Found 4 observations with a pareto_k > 0.7 in model '.'. It is
## recommended to set 'moment_match = TRUE' in order to perform moment matching
## for problematic observations.

## 
## Computed from 2400 by 2070 log-likelihood matrix
## 
##          Estimate    SE
## elpd_loo  -2151.2  62.1
## p_loo        62.0   5.7
## looic      4302.4 124.3
## ------
## Monte Carlo SE of elpd_loo is NA.
## 
## Pareto k diagnostic values:
##                          Count Pct.    Min. n_eff
## (-Inf, 0.5]   (good)     2055  99.3%   431       
##  (0.5, 0.7]   (ok)         11   0.5%   88        
##    (0.7, 1]   (bad)         4   0.2%   43        
##    (1, Inf)   (very bad)    0   0.0%   <NA>      
## See help('pareto-k-diagnostic') for details.

(m.3b <- methods.det.brm3b %>% loo())

## Warning: Found 3 observations with a pareto_k > 0.7 in model '.'. It is
## recommended to set 'moment_match = TRUE' in order to perform moment matching
## for problematic observations.

## 
## Computed from 2400 by 2070 log-likelihood matrix
## 
##          Estimate    SE
## elpd_loo  -2150.4  62.1
## p_loo        61.2   5.6
## looic      4300.7 124.1
## ------
## Monte Carlo SE of elpd_loo is NA.
## 
## Pareto k diagnostic values:
##                          Count Pct.    Min. n_eff
## (-Inf, 0.5]   (good)     2059  99.5%   281       
##  (0.5, 0.7]   (ok)          8   0.4%   139       
##    (0.7, 1]   (bad)         3   0.1%   46        
##    (1, Inf)   (very bad)    0   0.0%   <NA>      
## See help('pareto-k-diagnostic') for details.

loo_compare(loo(methods.det.brm1b), loo(methods.det.brm2b), loo(methods.det.brm3b))

## Warning: Found 14 observations with a pareto_k > 0.7 in model
## 'methods.det.brm1b'. It is recommended to set 'moment_match = TRUE' in order to
## perform moment matching for problematic observations.

## Warning: Found 4 observations with a pareto_k > 0.7 in model
## 'methods.det.brm2b'. It is recommended to set 'moment_match = TRUE' in order to
## perform moment matching for problematic observations.

## Warning: Found 3 observations with a pareto_k > 0.7 in model
## 'methods.det.brm3b'. It is recommended to set 'moment_match = TRUE' in order to
## perform moment matching for problematic observations.

##                   elpd_diff se_diff
## methods.det.brm3b    0.0       0.0 
## methods.det.brm2b   -0.8       0.4 
## methods.det.brm1b -904.0      93.9

Model methods.det.brm2b was selected as best model based on loo estimates.

7.2.3 Diagnostics

7.2.3.1 Trace plots

methods.det.brm2b$fit %>% stan_trace()

#### Autocorrelation plots

methods.det.brm2b$fit %>% stan_ac()

#### Rhat statistic

methods.det.brm2b$fit %>% stan_rhat()

#### Effective sampling size

methods.det.brm2b$fit %>% stan_ess()

#### Posterior predictive check plot

methods.det.brm2b %>% pp_check(x="lat", type="intervals")

#### DHARMa residuals

set.seed(5)
preds <- posterior_predict(methods.det.brm2b,  ndraws=250,  summary=FALSE)
method.resids <- createDHARMa(simulatedResponse = t(preds),
                            observedResponse = det.plot.groups$days.present,
                            fittedPredictedResponse = apply(preds, 2, median),
                            integerResponse = TRUE)
method.resids %>% plot()

#### Dispersion test

method.resids %>% testDispersion()

## 
##  DHARMa nonparametric dispersion test via sd of residuals fitted vs.
##  simulated
## 
## data:  simulationOutput
## dispersion = 0.4148, p-value = 0.04
## alternative hypothesis: two.sided

7.2.3.2 Zero-inflation test

method.resids %>% testZeroInflation()

## 
##  DHARMa zero-inflation test via comparison to expected zeros with
##  simulation under H0 = fitted model
## 
## data:  simulationOutput
## ratioObsSim = 0.99494, p-value = 0.816
## alternative hypothesis: two.sided

7.2.4 Investigation

7.2.4.1 Methods pairwise comparison for the average latitude

(diff.det.meth.avg <- methods.det.brm2b %>%
  emmeans(~assessment.method|lat) %>% 
  regrid() %>%
  pairs() %>% 
  gather_emmeans_draws() %>% 
  mutate(Percent = 100 * (exp(.value)-1), f.change = exp(.value)) %>% 
  summarise("Average difference (%)" = median(Percent),
            "Average fractional change" = median(f.change),
            "Lower HDI" = HDInterval::hdi(f.change)[1],
            "Upper HDI" = HDInterval::hdi(f.change)[2],
            "Probability of difference" = sum(.value > 0)/n()) %>% 
   select(-lat))

## # A tibble: 15 × 6
## # Groups:   contrast [15]
##    contrast                   Average differen…¹ Avera…² Lower…³ Upper…⁴ Proba…⁵
##    <fct>                                   <dbl>   <dbl>   <dbl>   <dbl>   <dbl>
##  1 pitfall - funnel                        16.4    1.16    0.705   1.74  0.764  
##  2 pitfall - incidentals                  249.     3.49    2.01    6.16  1      
##  3 pitfall - spotlighting                 206.     3.06    1.93    5.21  1      
##  4 pitfall - cover board                  234.     3.34    2.02    5.94  1      
##  5 pitfall - camera                       318.     4.18    2.36    7.89  1      
##  6 funnel - incidentals                   200.     3.00    1.90    4.97  1      
##  7 funnel - spotlighting                  161.     2.61    1.72    4.13  1      
##  8 funnel - cover board                   186.     2.86    1.81    4.74  1      
##  9 funnel - camera                        257.     3.57    2.21    6.35  1      
## 10 incidentals - spotlighting             -12.5    0.875   0.756   0.974 0.00417
## 11 incidentals - cover board               -4.03   0.960   0.856   1.06  0.204  
## 12 incidentals - camera                    19.2    1.19    1.10    1.32  1      
## 13 spotlighting - cover board               9.83   1.10    0.972   1.26  0.937  
## 14 spotlighting - camera                   36.7    1.37    1.20    1.62  1      
## 15 cover board - camera                    24.5    1.25    1.13    1.41  1      
## # … with abbreviated variable names ¹`Average difference (%)`,
## #   ²`Average fractional change`, ³`Lower HDI`, ⁴`Upper HDI`,
## #   ⁵`Probability of difference`

7.3 Bayesian Analysis - across all methods for arboreal vs ground-dwelling reptiles

7.3.1 Fit model

7.3.1.1 Model 1

priors1 <- prior(normal(2,1.5), class  = "Intercept") +
  prior(normal(0,1.5), class = "b") +
  prior(student_t(3,0,1.5), class = "sd")

methods.form1 <- bf(days.present ~ assessment.method*lifestyle + offset(log(days)) + (1|site/site.plot) +
                      (1|scientific.name), family="negbinomial")

methods.det.life.brm1 <- brm(methods.form1,
                  data = det.plot.groups,
                  prior = priors1,
                  sample_prior = "only",
                  refresh = 0,
                  chains = 3, cores = 3,
                  iter = 5000,
                  thin = 5,
                  seed = 8,
                  warmup = 1000,
                  backend = 'cmdstanr')

## Running MCMC with 3 parallel chains...
## 
## Chain 1 finished in 3.2 seconds.
## Chain 2 finished in 3.9 seconds.
## Chain 3 finished in 3.8 seconds.
## 
## All 3 chains finished successfully.
## Mean chain execution time: 3.6 seconds.
## Total execution time: 3.9 seconds.

7.3.1.1.1 Predictions

methods.det.life.brm1 %>% ggpredict(~assessment.method|lifestyle) %>% plot(add.data = TRUE)

methods.det.life.brm1 %>% ggpredict(~lifestyle|assessment.method) %>% plot(add.data = TRUE)

7.3.1.1.2 Prior vs Posterior

methods.det.life.brm1b <- methods.det.life.brm1 %>%
  update(sample_prior = "yes",
         refresh = 0,
         seed = 8,
         cores = 3,
         backend = "cmdstanr")

## Running MCMC with 3 parallel chains...
## 
## Chain 3 finished in 36.6 seconds.
## Chain 1 finished in 38.7 seconds.
## Chain 2 finished in 54.2 seconds.
## 
## All 3 chains finished successfully.
## Mean chain execution time: 43.2 seconds.
## Total execution time: 54.2 seconds.

7.3.1.1.3 Predictions

methods.det.life.brm1b %>% ggpredict(~assessment.method|lifestyle) %>% plot(add.data = TRUE)

methods.det.life.brm1b %>% ggpredict(~lifestyle|assessment.method) %>% plot(add.data = TRUE)

7.3.1.2 Model 2

priors2 <- prior(normal(2,1.5), class  = "Intercept") +
  prior(normal(0,1.5), class = "b") +
  prior(student_t(3,0,1.5), class = "sd")

methods.form2 <- bf(days.present ~ assessment.method*lifestyle + offset(log(days)) + (1|site/site.plot) +
                      (1|scientific.name), family="negbinomial2")

methods.det.life.brm2 <- brm(methods.form2,
                  data = det.plot.groups,
                  prior = priors2,
                  sample_prior = "only",
                  refresh = 0,
                  chains = 3, cores = 3,
                  iter = 5000,
                  thin = 5,
                  seed = 8,
                  warmup = 1000,
                  backend = 'cmdstanr')

## Running MCMC with 3 parallel chains...
## 
## Chain 1 finished in 0.5 seconds.
## Chain 2 finished in 0.5 seconds.
## Chain 3 finished in 0.5 seconds.
## 
## All 3 chains finished successfully.
## Mean chain execution time: 0.5 seconds.
## Total execution time: 0.6 seconds.

7.3.1.2.1 Predictions

methods.det.life.brm2 %>% ggpredict(~assessment.method|lifestyle) %>% plot(add.data = TRUE)

methods.det.life.brm2 %>% ggpredict(~lifestyle|assessment.method) %>% plot(add.data = TRUE)

7.3.1.2.2 Prior vs Posterior

methods.det.life.brm2b <- methods.det.life.brm2 %>%
  update(sample_prior = "yes",
         refresh = 0,
         seed = 8,
         cores = 3,
         backend = "cmdstanr")

## Running MCMC with 3 parallel chains...
## 
## Chain 2 finished in 35.8 seconds.
## Chain 1 finished in 37.1 seconds.
## Chain 3 finished in 38.3 seconds.
## 
## All 3 chains finished successfully.
## Mean chain execution time: 37.1 seconds.
## Total execution time: 38.4 seconds.

7.3.1.2.3 Predictions

methods.det.life.brm2b %>% ggpredict(~assessment.method|lifestyle) %>% plot(add.data = TRUE)

methods.det.life.brm2b %>% ggpredict(~lifestyle|assessment.method) %>% plot(add.data = TRUE)

7.3.1.3 Compare Models

(m.1b <- methods.det.life.brm1b %>% loo())

## Warning: Found 2 observations with a pareto_k > 0.7 in model '.'. It is
## recommended to set 'moment_match = TRUE' in order to perform moment matching
## for problematic observations.

## 
## Computed from 2400 by 2070 log-likelihood matrix
## 
##          Estimate    SE
## elpd_loo  -1993.0  58.4
## p_loo        66.6   5.6
## looic      3985.9 116.7
## ------
## Monte Carlo SE of elpd_loo is NA.
## 
## Pareto k diagnostic values:
##                          Count Pct.    Min. n_eff
## (-Inf, 0.5]   (good)     2061  99.6%   64        
##  (0.5, 0.7]   (ok)          7   0.3%   150       
##    (0.7, 1]   (bad)         2   0.1%   27        
##    (1, Inf)   (very bad)    0   0.0%   <NA>      
## See help('pareto-k-diagnostic') for details.

(m.2b <- methods.det.life.brm2b %>% loo())

## Warning: Found 4 observations with a pareto_k > 0.7 in model '.'. It is
## recommended to set 'moment_match = TRUE' in order to perform moment matching
## for problematic observations.

## 
## Computed from 2400 by 2070 log-likelihood matrix
## 
##          Estimate    SE
## elpd_loo  -1992.6  58.3
## p_loo        65.8   5.5
## looic      3985.2 116.7
## ------
## Monte Carlo SE of elpd_loo is NA.
## 
## Pareto k diagnostic values:
##                          Count Pct.    Min. n_eff
## (-Inf, 0.5]   (good)     2062  99.6%   417       
##  (0.5, 0.7]   (ok)          4   0.2%   163       
##    (0.7, 1]   (bad)         4   0.2%   47        
##    (1, Inf)   (very bad)    0   0.0%   <NA>      
## See help('pareto-k-diagnostic') for details.

loo_compare(loo(methods.det.life.brm1b), loo(methods.det.life.brm2b))

## Warning: Found 2 observations with a pareto_k > 0.7 in model
## 'methods.det.life.brm1b'. It is recommended to set 'moment_match = TRUE' in
## order to perform moment matching for problematic observations.

## Warning: Found 4 observations with a pareto_k > 0.7 in model
## 'methods.det.life.brm2b'. It is recommended to set 'moment_match = TRUE' in
## order to perform moment matching for problematic observations.

##                        elpd_diff se_diff
## methods.det.life.brm2b  0.0       0.0   
## methods.det.life.brm1b -0.4       0.4

Model methods.det.life.brm1b was selected as best model based on loo estimates.

7.3.2 Diagnostics

7.3.2.1 Trace plots

methods.det.life.brm1b$fit %>% stan_trace()

#### Autocorrelation plots

methods.det.life.brm1b$fit %>% stan_ac()

#### Rhat statistic

methods.det.life.brm1b$fit %>% stan_rhat()

#### Effective sampling size

methods.det.life.brm1b$fit %>% stan_ess()

7.3.2.2 DHARMa residuals

set.seed(5)
preds <- posterior_predict(methods.det.life.brm2b,  ndraws=250,  summary=FALSE)
method.resids <- createDHARMa(simulatedResponse = t(preds),
                            observedResponse = det.plot.groups$days.present,
                            fittedPredictedResponse = apply(preds, 2, median),
                            integerResponse = TRUE)
method.resids %>% plot()

#### Dispersion test

method.resids %>% testDispersion()

## 
##  DHARMa nonparametric dispersion test via sd of residuals fitted vs.
##  simulated
## 
## data:  simulationOutput
## dispersion = 0.85807, p-value = 0.744
## alternative hypothesis: two.sided

7.3.2.3 Zero-inflation test

method.resids %>% testZeroInflation()

## 
##  DHARMa zero-inflation test via comparison to expected zeros with
##  simulation under H0 = fitted model
## 
## data:  simulationOutput
## ratioObsSim = 1.0058, p-value = 0.776
## alternative hypothesis: two.sided

7.3.3 Investigation

(diff.det.life.meth <- methods.det.life.brm2b %>%
  emmeans(~assessment.method|lifestyle) %>% 
  regrid() %>%
  pairs() %>% 
  #pairs(reverse = TRUE) %>% to reverse the contrasts 
  gather_emmeans_draws() %>% 
  mutate(Percent = 100 * (exp(.value)-1), f.change = exp(.value)) %>%
  summarise("Average fractional change" = median(f.change),
            "Lower HDI" = HDInterval::hdi(f.change)[1],
            "Upper HDI" = HDInterval::hdi(f.change)[2],
            "Probability of difference" = sum(.value > 0)/n()) %>% 
  arrange(lifestyle))

## # A tibble: 30 × 6
## # Groups:   contrast [15]
##    contrast                   lifestyle        Average…¹ Lower…² Upper…³ Proba…⁴
##    <fct>                      <fct>                <dbl>   <dbl>   <dbl>   <dbl>
##  1 pitfall - funnel           Arboreal Species     1.89   1.23     3.26  1   e+0
##  2 pitfall - incidentals      Arboreal Species     1.77   1.18     2.85  1   e+0
##  3 pitfall - spotlighting     Arboreal Species     0.463  0.138    0.817 6.25e-3
##  4 pitfall - cover board      Arboreal Species     0.343  0.0817   0.627 4.17e-4
##  5 pitfall - camera           Arboreal Species     2.30   1.47     4.24  1   e+0
##  6 funnel - incidentals       Arboreal Species     0.937  0.733    1.14  2.45e-1
##  7 funnel - spotlighting      Arboreal Species     0.242  0.0488   0.440 0      
##  8 funnel - cover board       Arboreal Species     0.180  0.0274   0.359 0      
##  9 funnel - camera            Arboreal Species     1.21   1.06     1.44  1   e+0
## 10 incidentals - spotlighting Arboreal Species     0.258  0.0560   0.454 0      
## # … with 20 more rows, and abbreviated variable names
## #   ¹`Average fractional change`, ²`Lower HDI`, ³`Upper HDI`,
## #   ⁴`Probability of difference`

7.4 Visualisation

pal <- c("#FF8300", "#D14103","#0CC170","black","#4E84C4","#8348D8")

(det.life.plot <- ggplot(det.plot.groups, aes(x=assessment.method,y=det.prob)) +
  geom_boxplot(aes(color = assessment.method,
                   color = after_scale(darken(color, .1, space = "HLS")),
                   fill = after_scale(desaturate(lighten(color, .8), .4))),
             width = .2, outlier.shape = NA) +
  gghalves::geom_half_point(aes(color = assessment.method, color = after_scale(darken(color, .1, space = "HLS"))), fill = "white", shape = 21, stroke = .4, size = 2, side = "1",
                            transformation = PositionIdentity) +
    gghalves::geom_half_point(aes(fill = assessment.method), color = "transparent", shape = 21, stroke = .4, size = 2, alpha = .3, side = "1", transformation = PositionIdentity) +
  facet_wrap(~lifestyle) +
  scale_y_continuous(labels = scales::percent,
                     breaks = seq(0, 0.9, by = 0.1),
                     limits = c(0,0.9),
                     name = "Detection Probability") +
  scale_x_discrete(name = "", guide = "none") +
  scale_fill_manual(values = pal, guide = "none") +
  scale_colour_manual(values = pal, name = "", labels = c("Pitfall Trap","Funnel Trap","Incidental","Spotlighting","Arboreal Cover Board","Camera Trap")) +
  my.theme() +
  theme(panel.grid.major.y = element_line(colour = "grey", linewidth = 0.2, linetype = "dotted"),
        panel.grid.minor.y = element_line(colour = "grey", linewidth = 0.1, linetype = "dotted"),
        legend.position = c(0.5, -0.07),
        legend.background = element_rect(fill = "transparent"),
        legend.direction = "horizontal",
        plot.margin = unit(c(5, 10, 12, 10), units = "mm"),
        panel.border = element_rect(fill = NA, color = "black"),
        strip.background = element_rect(fill = "lightgrey")))

## Warning: Duplicated aesthetics after name standardisation: colour
## Duplicated aesthetics after name standardisation: colour

8 Session Info

sessionInfo()

## R version 4.2.2 (2022-10-31)
## Platform: aarch64-apple-darwin20 (64-bit)
## Running under: macOS Ventura 13.2.1
## 
## Matrix products: default
## BLAS:   /Library/Frameworks/R.framework/Versions/4.2-arm64/Resources/lib/libRblas.0.dylib
## LAPACK: /Library/Frameworks/R.framework/Versions/4.2-arm64/Resources/lib/libRlapack.dylib
## 
## locale:
## [1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8
## 
## attached base packages:
## [1] stats     graphics  grDevices utils     datasets  methods   base     
## 
## other attached packages:
##  [1] performance_0.10.0   loo_2.5.1            gghalves_0.1.4      
##  [4] ggridges_0.5.4       report_0.5.5         knitr_1.42          
##  [7] MuMIn_1.46.0         colorspace_2.1-0     scales_1.2.1        
## [10] EcolUtils_0.1        corrplot_0.92        GGally_2.1.2        
## [13] ggrepel_0.9.1        ggvegan_0.1-0        car_3.1-0           
## [16] carData_3.0-5        vegan_2.6-4          lattice_0.20-45     
## [19] permute_0.9-7        reshape2_1.4.4       see_0.7.1           
## [22] bayestestR_0.12.1    patchwork_1.1.1      posterior_1.3.1     
## [25] broom.mixed_0.2.9.4  ggeffects_1.1.3      HDInterval_0.2.2    
## [28] tidybayes_3.0.2      broom_1.0.0          emmeans_1.7.5       
## [31] rstan_2.21.7         StanHeaders_2.21.0-7 DHARMa_0.4.5        
## [34] bayesplot_1.9.0      coda_0.19-4          standist_0.0.0.9000 
## [37] brms_2.18.0          Rcpp_1.0.10          cmdstanr_0.5.3      
## [40] forcats_0.5.1        stringr_1.5.0        dplyr_1.1.0         
## [43] purrr_1.0.1          readr_2.1.2          tidyr_1.3.0         
## [46] tibble_3.1.8         ggplot2_3.4.1        tidyverse_1.3.2     
## 
## loaded via a namespace (and not attached):
##   [1] utf8_1.2.3           tidyselect_1.2.0     lme4_1.1-30         
##   [4] htmlwidgets_1.6.1    grid_4.2.2           munsell_0.5.0       
##   [7] effectsize_0.7.0     codetools_0.2-18     DT_0.26             
##  [10] future_1.27.0        miniUI_0.1.1.1       withr_2.5.0         
##  [13] Brobdingnag_1.2-9    qgam_1.3.4           highr_0.10          
##  [16] rstudioapi_0.14      stats4_4.2.2         listenv_0.8.0       
##  [19] labeling_0.4.2       farver_2.1.1         datawizard_0.6.3    
##  [22] gap.datasets_0.0.5   bridgesampling_1.1-2 parallelly_1.32.1   
##  [25] vctrs_0.5.2          generics_0.1.3       xfun_0.37           
##  [28] doParallel_1.0.17    R6_2.5.1             markdown_1.1        
##  [31] cachem_1.0.7         reshape_0.8.9        assertthat_0.2.1    
##  [34] promises_1.2.0.1     googlesheets4_1.0.0  gtable_0.3.1        
##  [37] globals_0.15.1       processx_3.8.0       rlang_1.0.6         
##  [40] splines_4.2.2        gargle_1.2.0         checkmate_2.1.0     
##  [43] inline_0.3.19        yaml_2.3.7           abind_1.4-5         
##  [46] modelr_0.1.8         threejs_0.3.3        crosstalk_1.2.0     
##  [49] backports_1.4.1      httpuv_1.6.5         tensorA_0.36.2      
##  [52] tools_4.2.2          ellipsis_0.3.2       jquerylib_0.1.4     
##  [55] RColorBrewer_1.1-3   plyr_1.8.7           base64enc_0.1-3     
##  [58] ps_1.7.2             prettyunits_1.1.1    zoo_1.8-10          
##  [61] haven_2.5.0          cluster_2.1.4        fs_1.6.1            
##  [64] furrr_0.3.0          magrittr_2.0.3       data.table_1.14.8   
##  [67] ggdist_3.2.0         colourpicker_1.1.1   reprex_2.0.1        
##  [70] googledrive_2.0.0    mvtnorm_1.1-3        matrixStats_0.62.0  
##  [73] hms_1.1.1            shinyjs_2.1.0        mime_0.12           
##  [76] evaluate_0.20        arrayhelpers_1.1-0   xtable_1.8-4        
##  [79] shinystan_2.6.0      readxl_1.4.0         gridExtra_2.3       
##  [82] rstantools_2.2.0     compiler_4.2.2       crayon_1.5.2        
##  [85] minqa_1.2.4          htmltools_0.5.4      mgcv_1.8-41         
##  [88] later_1.3.0          tzdb_0.3.0           RcppParallel_5.1.5  
##  [91] lubridate_1.8.0      DBI_1.1.3            sjlabelled_1.2.0    
##  [94] dbplyr_2.2.1         MASS_7.3-58.1        boot_1.3-28         
##  [97] Matrix_1.5-3         cli_3.6.0            parallel_4.2.2      
## [100] insight_0.18.6       igraph_1.3.5         pkgconfig_2.0.3     
## [103] foreach_1.5.2        xml2_1.3.3           svUnit_1.0.6        
## [106] dygraphs_1.1.1.6     bslib_0.4.2          estimability_1.4    
## [109] rvest_1.0.3          snakecase_0.11.0     distributional_0.3.0
## [112] callr_3.7.3          digest_0.6.31        parameters_0.19.0   
## [115] rmarkdown_2.20       cellranger_1.1.0     gap_1.2.3-6         
## [118] shiny_1.7.2          gtools_3.9.4         nloptr_2.0.3        
## [121] lifecycle_1.0.3      nlme_3.1-160         jsonlite_1.8.4      
## [124] fansi_1.0.4          pillar_1.8.1         fastmap_1.1.1       
## [127] httr_1.4.5           pkgbuild_1.3.1       glue_1.6.2          
## [130] xts_0.12.2           iterators_1.0.14     shinythemes_1.2.0   
## [133] stringi_1.7.12       sass_0.4.5

9 Cite Packages

cite_packages()

## Warning in utils::citation(pkg_name): no date field in DESCRIPTION file of
## package 'standist'

##   - Bartoń K (2022). _MuMIn: Multi-Model Inference_. R package version1.46.0, <https://CRAN.R-project.org/package=MuMIn>.
##   - Bolker B, Robinson D (2022). _broom.mixed: Tidying Methods for MixedModels_. R package version 0.2.9.4,<https://CRAN.R-project.org/package=broom.mixed>.
##   - Bürkner P (2017). "brms: An R Package for Bayesian Multilevel ModelsUsing Stan." _Journal of Statistical Software_, *80*(1), 1-28.doi:10.18637/jss.v080.i01 <https://doi.org/10.18637/jss.v080.i01>.Bürkner P (2018). "Advanced Bayesian Multilevel Modeling with the RPackage brms." _The R Journal_, *10*(1), 395-411.doi:10.32614/RJ-2018-017 <https://doi.org/10.32614/RJ-2018-017>.Bürkner P (2021). "Bayesian Item Response Modeling in R with brms andStan." _Journal of Statistical Software_, *100*(5), 1-54.doi:10.18637/jss.v100.i05 <https://doi.org/10.18637/jss.v100.i05>.
##   - Bürkner P, Gabry J, Kay M, Vehtari A (2022). "posterior: Tools forWorking with Posterior Distributions." R package version 1.3.1,<https://mc-stan.org/posterior/>.Vehtari A, Gelman A, Simpson D, Carpenter B, Bürkner P (2021)."Rank-normalization, folding, and localization: An improved Rhat forassessing convergence of MCMC (with discussion)." _Bayesian Analysis_.
##   - Eddelbuettel D, François R (2011). "Rcpp: Seamless R and C++Integration." _Journal of Statistical Software_, *40*(8), 1-18.doi:10.18637/jss.v040.i08 <https://doi.org/10.18637/jss.v040.i08>.Eddelbuettel D (2013). _Seamless R and C++ Integration with Rcpp_.Springer, New York. doi:10.1007/978-1-4614-6868-4<https://doi.org/10.1007/978-1-4614-6868-4>, ISBN 978-1-4614-6867-7.Eddelbuettel D, Balamuta JJ (2018). "Extending extitR with extitC++: ABrief Introduction to extitRcpp." _The American Statistician_, *72*(1),28-36. doi:10.1080/00031305.2017.1375990<https://doi.org/10.1080/00031305.2017.1375990>.
##   - Fox J, Weisberg S (2019). _An R Companion to Applied Regression_, Thirdedition. Sage, Thousand Oaks CA.<https://socialsciences.mcmaster.ca/jfox/Books/Companion/>.
##   - Fox J, Weisberg S, Price B (2022). _carData: Companion to AppliedRegression Data Sets_. R package version 3.0-5,<https://CRAN.R-project.org/package=carData>.
##   - Gabry J, Češnovar R (2022). _cmdstanr: R Interface to 'CmdStan'_.https://mc-stan.org/cmdstanr/, https://discourse.mc-stan.org.
##   - Gabry J, Mahr T (2022). "bayesplot: Plotting for Bayesian Models." Rpackage version 1.9.0, <https://mc-stan.org/bayesplot/>.Gabry J, Simpson D, Vehtari A, Betancourt M, Gelman A (2019)."Visualization in Bayesian workflow." _J. R. Stat. Soc. A_, *182*,389-402. doi:10.1111/rssa.12378 <https://doi.org/10.1111/rssa.12378>.
##   - Girard J (2022). _standist: What the Package Does (One Line, TitleCase)_. R package version 0.0.0.9000.
##   - Hartig F (2022). _DHARMa: Residual Diagnostics for Hierarchical(Multi-Level / Mixed) Regression Models_. R package version 0.4.5,<https://CRAN.R-project.org/package=DHARMa>.
##   - Kay M (2022). _tidybayes: Tidy Data and Geoms for Bayesian Models_.doi:10.5281/zenodo.1308151 <https://doi.org/10.5281/zenodo.1308151>, Rpackage version 3.0.2, <http://mjskay.github.io/tidybayes/>.
##   - Lenth R (2022). _emmeans: Estimated Marginal Means, aka Least-SquaresMeans_. R package version 1.7.5,<https://CRAN.R-project.org/package=emmeans>.
##   - Lüdecke D (2018). "ggeffects: Tidy Data Frames of Marginal Effects fromRegression Models." _Journal of Open Source Software_, *3*(26), 772.doi:10.21105/joss.00772 <https://doi.org/10.21105/joss.00772>.
##   - Lüdecke D, Ben-Shachar M, Patil I, Waggoner P, Makowski D (2021)."performance: An R Package for Assessment, Comparison and Testing ofStatistical Models." _Journal of Open Source Software_, *6*(60), 3139.doi:10.21105/joss.03139 <https://doi.org/10.21105/joss.03139>.
##   - Lüdecke D, Patil I, Ben-Shachar M, Wiernik B, Waggoner P, Makowski D(2021). "see: An R Package for Visualizing Statistical Models."_Journal of Open Source Software_, *6*(64), 3393.doi:10.21105/joss.03393 <https://doi.org/10.21105/joss.03393>.
##   - Makowski D, Ben-Shachar M, Lüdecke D (2019). "bayestestR: DescribingEffects and their Uncertainty, Existence and Significance within theBayesian Framework." _Journal of Open Source Software_, *4*(40), 1541.doi:10.21105/joss.01541 <https://doi.org/10.21105/joss.01541>,<https://joss.theoj.org/papers/10.21105/joss.01541>.
##   - Makowski D, Ben-Shachar M, Patil I, Lüdecke D (2021). "AutomatedResults Reporting as a Practical Tool to Improve Reproducibility andMethodological Best Practices Adoption." _CRAN_.<https://github.com/easystats/report>.
##   - Meredith M, Kruschke J (2020). _HDInterval: Highest (Posterior) DensityIntervals_. R package version 0.2.2,<https://CRAN.R-project.org/package=HDInterval>.
##   - Müller K, Wickham H (2022). _tibble: Simple Data Frames_. R packageversion 3.1.8, <https://CRAN.R-project.org/package=tibble>.
##   - Oksanen J, Simpson G, Blanchet F, Kindt R, Legendre P, Minchin P,O'Hara R, Solymos P, Stevens M, Szoecs E, Wagner H, Barbour M, BedwardM, Bolker B, Borcard D, Carvalho G, Chirico M, De Caceres M, Durand S,Evangelista H, FitzJohn R, Friendly M, Furneaux B, Hannigan G, Hill M,Lahti L, McGlinn D, Ouellette M, Ribeiro Cunha E, Smith T, Stier A, TerBraak C, Weedon J (2022). _vegan: Community Ecology Package_. R packageversion 2.6-4, <https://CRAN.R-project.org/package=vegan>.
##   - Pedersen T (2020). _patchwork: The Composer of Plots_. R packageversion 1.1.1, <https://CRAN.R-project.org/package=patchwork>.
##   - Plummer M, Best N, Cowles K, Vines K (2006). "CODA: ConvergenceDiagnosis and Output Analysis for MCMC." _R News_, *6*(1), 7-11.<https://journal.r-project.org/archive/>.
##   - R Core Team (2022). _R: A Language and Environment for StatisticalComputing_. R Foundation for Statistical Computing, Vienna, Austria.<https://www.R-project.org/>.
##   - Robinson D, Hayes A, Couch S (2022). _broom: Convert StatisticalObjects into Tidy Tibbles_. R package version 1.0.0,<https://CRAN.R-project.org/package=broom>.
##   - Salazar G (2022). _EcolUtils: Utilities for community ecologyanalysis_. R package version 0.1,<https://github.com/GuillemSalazar/EcolUtils>.
##   - Sarkar D (2008). _Lattice: Multivariate Data Visualization with R_.Springer, New York. ISBN 978-0-387-75968-5,<http://lmdvr.r-forge.r-project.org>.
##   - Schloerke B, Cook D, Larmarange J, Briatte F, Marbach M, Thoen E,Elberg A, Crowley J (2021). _GGally: Extension to 'ggplot2'_. R packageversion 2.1.2, <https://CRAN.R-project.org/package=GGally>.
##   - Simpson G (2019). _ggvegan: 'ggplot2' Plots for the 'vegan' Package_. Rpackage version 0.1-0.
##   - Simpson G (2022). _permute: Functions for Generating RestrictedPermutations of Data_. R package version 0.9-7,<https://CRAN.R-project.org/package=permute>.
##   - Slowikowski K (2021). _ggrepel: Automatically Position Non-OverlappingText Labels with 'ggplot2'_. R package version 0.9.1,<https://CRAN.R-project.org/package=ggrepel>.
##   - Stan Development Team (2020). "StanHeaders: Headers for the R interfaceto Stan." R package version 2.21.0-6, <https://mc-stan.org/>.
##   - Stan Development Team (2022). "RStan: the R interface to Stan." Rpackage version 2.21.7, <https://mc-stan.org/>.
##   - Tiedemann F (2022). _gghalves: Compose Half-Half Plots Using YourFavourite Geoms_. R package version 0.1.4,<https://CRAN.R-project.org/package=gghalves>.
##   - Vehtari A, Gabry J, Magnusson M, Yao Y, Bürkner P, Paananen T, Gelman A(2022). "loo: Efficient leave-one-out cross-validation and WAIC forBayesian models." R package version 2.5.1, <https://mc-stan.org/loo/>.Vehtari A, Gelman A, Gabry J (2017). "Practical Bayesian modelevaluation using leave-one-out cross-validation and WAIC." _Statisticsand Computing_, *27*, 1413-1432. doi:10.1007/s11222-016-9696-4<https://doi.org/10.1007/s11222-016-9696-4>.Yao Y, Vehtari A, Simpson D, Gelman A (2017). "Using stacking toaverage Bayesian predictive distributions." _Bayesian Analysis_.doi:10.1214/17-BA1091 <https://doi.org/10.1214/17-BA1091>.
##   - Wei T, Simko V (2021). _R package 'corrplot': Visualization of aCorrelation Matrix_. (Version 0.92),<https://github.com/taiyun/corrplot>.
##   - Wickham H (2007). "Reshaping Data with the reshape Package." _Journalof Statistical Software_, *21*(12), 1-20.<http://www.jstatsoft.org/v21/i12/>.
##   - Wickham H (2016). _ggplot2: Elegant Graphics for Data Analysis_.Springer-Verlag New York. ISBN 978-3-319-24277-4,<https://ggplot2.tidyverse.org>.
##   - Wickham H (2021). _forcats: Tools for Working with CategoricalVariables (Factors)_. R package version 0.5.1,<https://CRAN.R-project.org/package=forcats>.
##   - Wickham H (2022). _stringr: Simple, Consistent Wrappers for CommonString Operations_. R package version 1.5.0,<https://CRAN.R-project.org/package=stringr>.
##   - Wickham H, Averick M, Bryan J, Chang W, McGowan LD, François R,Grolemund G, Hayes A, Henry L, Hester J, Kuhn M, Pedersen TL, Miller E,Bache SM, Müller K, Ooms J, Robinson D, Seidel DP, Spinu V, TakahashiK, Vaughan D, Wilke C, Woo K, Yutani H (2019). "Welcome to thetidyverse." _Journal of Open Source Software_, *4*(43), 1686.doi:10.21105/joss.01686 <https://doi.org/10.21105/joss.01686>.
##   - Wickham H, François R, Henry L, Müller K, Vaughan D (2023). _dplyr: AGrammar of Data Manipulation_. R package version 1.1.0,<https://CRAN.R-project.org/package=dplyr>.
##   - Wickham H, Henry L (2023). _purrr: Functional Programming Tools_. Rpackage version 1.0.1, <https://CRAN.R-project.org/package=purrr>.
##   - Wickham H, Hester J, Bryan J (2022). _readr: Read Rectangular TextData_. R package version 2.1.2,<https://CRAN.R-project.org/package=readr>.
##   - Wickham H, Seidel D (2022). _scales: Scale Functions forVisualization_. R package version 1.2.1,<https://CRAN.R-project.org/package=scales>.
##   - Wickham H, Vaughan D, Girlich M (2023). _tidyr: Tidy Messy Data_. Rpackage version 1.3.0, <https://CRAN.R-project.org/package=tidyr>.
##   - Wilke C (2022). _ggridges: Ridgeline Plots in 'ggplot2'_. R packageversion 0.5.4, <https://CRAN.R-project.org/package=ggridges>.
##   - Xie Y (2023). _knitr: A General-Purpose Package for Dynamic ReportGeneration in R_. R package version 1.42, <https://yihui.org/knitr/>.Xie Y (2015). _Dynamic Documents with R and knitr_, 2nd edition.Chapman and Hall/CRC, Boca Raton, Florida. ISBN 978-1498716963,<https://yihui.org/knitr/>.Xie Y (2014). "knitr: A Comprehensive Tool for Reproducible Research inR." In Stodden V, Leisch F, Peng RD (eds.), _Implementing ReproducibleComputational Research_. Chapman and Hall/CRC. ISBN 978-1466561595.
##   - Zeileis A, Fisher JC, Hornik K, Ihaka R, McWhite CD, Murrell P,Stauffer R, Wilke CO (2020). "colorspace: A Toolbox for Manipulatingand Assessing Colors and Palettes." _Journal of Statistical Software_,*96*(1), 1-49. doi:10.18637/jss.v096.i01<https://doi.org/10.18637/jss.v096.i01>.Zeileis A, Hornik K, Murrell P (2009). "Escaping RGBland: SelectingColors for Statistical Graphics." _Computational Statistics \& DataAnalysis_, *53*(9), 3259-3270. doi:10.1016/j.csda.2008.11.033<https://doi.org/10.1016/j.csda.2008.11.033>.Stauffer R, Mayr GJ, Dabernig M, Zeileis A (2009). "Somewhere over theRainbow: How to Make Effective Use of Colors in MeteorologicalVisualizations." _Bulletin of the American Meteorological Society_,*96*(2), 203-216. doi:10.1175/BAMS-D-13-00155.1<https://doi.org/10.1175/BAMS-D-13-00155.1>.

Hoefer et al 2023 - Sampling Methods in Reptiles

Sebastian Hoefer

2023-04-04

1 Load packages

2 Functions

3 Load data

4 Species Richness

4.1 Prepare data

4.2 Bayesian Analysis

4.2.1 Priors

4.2.2 Fit model

4.2.2.1 Model 1

4.2.2.1.1 Predictions

4.2.2.1.2 Prior vs Posterior

4.2.2.1.3 Predictions

4.2.2.2 Model 2

4.2.2.2.1 Predictions

4.2.2.2.2 Prior vs Posterior

4.2.2.2.3 Predictions

4.2.2.3 Model 3

4.2.2.3.1 Predictions

4.2.2.3.2 Prior vs Posterior

4.2.2.3.3 Predictions

4.2.2.4 Compare Models

4.2.3 Diagnostics

4.2.3.1 Trace plots

4.2.3.2 Zero-inflation test

4.2.4 Investigation

4.2.4.1 Methods pairwise comparison for each site

4.2.4.2 Methods pairwise comparison for the average latitude

4.2.5 Summary Plot

4.2.6 Report

5 Survey Effort

5.1 Prepare data

5.2 Loop

5.3 Visualisation

6 Community composition

6.1 Prepare data

6.2 NMDS Ordination

6.2.1 Bray-Curtis dissimilarity

6.2.2 Jaccard dissimilarity

6.3 Visualisation

6.3.1 Bray-Curtis dissimilarity

6.3.2 Jaccard dissimilarity

6.4 Investigation

6.5 Adonis

6.5.1 Bray-Curtis dissimilarity

6.5.2 Jaccard dissimilarity

7 Detection probability

7.1 Prepare data

7.2 Bayesian Analysis - across all methods for all reptiles

7.2.1 Priors

7.2.2 Fit model

7.2.2.1 Model 1

7.2.2.1.1 Predictions

7.2.2.1.2 Prior vs Posterior

7.2.2.1.3 Predictions

7.2.2.2 Model 2

7.2.2.2.1 Predictions

7.2.2.2.2 Prior vs Posterior

7.2.2.2.3 Predictions

7.2.2.3 Model 3

7.2.2.3.1 Predictions

7.2.2.3.2 Prior vs Posterior

7.2.2.3.3 Predictions

7.2.2.4 Compare Models

7.2.3 Diagnostics

7.2.3.1 Trace plots

7.2.3.2 Zero-inflation test

7.2.4 Investigation

7.2.4.1 Methods pairwise comparison for the average latitude

7.3 Bayesian Analysis - across all methods for arboreal vs ground-dwelling reptiles

7.3.1 Fit model

7.3.1.1 Model 1

7.3.1.1.1 Predictions

7.3.1.1.2 Prior vs Posterior

7.3.1.1.3 Predictions

7.3.1.2 Model 2

7.3.1.2.1 Predictions

7.3.1.2.2 Prior vs Posterior